Click here👆to get an answer to your question ️ A solution of the equation (1 tan x )(1 tan x) sec^2x 2^tan^2 = 0 , where x lies in the interval pi2, pi2 is given by$$\int sec^2x \tan^2x dx = tan^2x 2\int \sec^2x \tan^2x dx$$ You can move the $ 2\int \sec^2x \tan^2x dx$ to the left hand side of the equation by addition $$\int \sec^2x \tan^2x dx 2\int \sec^2x \tan^2x dx= tan^2x c, c\in\mathbb{R}$$ Note that once we have a side without an integral on it you need to include a constant of integrationRewrite sec(x) sec ( x) in terms of sines and cosines Rewrite tan(x) tan ( x) in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by 1 cos(x) 1 cos ( x) Write cos(x) cos ( x) as a fraction with denominator 1 1 Cancel the common factor of cos(x) cos ( x)
Integrate Sec 2x Method 2
Tan^2(x) + 1 = sec^2(x) proof
Tan^2(x) + 1 = sec^2(x) proof-About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us Creators prove that cot x tan 2x1 =sec 2x Trigonometry Verify the identity algebraically TAN X COT Y/TAN X COT Y= TAN Y COT X Math Factorthen use fundamental identities to simplify the expression below and determine which of the following is not equivalent cot^2 a * tan^2 a cot^2 a A csc^ 2 alpha B1/ sin^ 2 alpha C1/ 1cos^ 2 alpha D
Unlock StepbyStep derivative of sec^2 (x) Extended Keyboard Examples heart 22 profile rohinishiva17 Answer LHS= (sec^2)^3 (tan^2)^3 = (sec^2tan^2)^33sec^2*tan^2 (sec^2tan^2) = (1)^33 (1tan^2x)tan^2x (1) (sec^2xtan^2x)=1In this video you will learn how to verify trigonometric identitiesverifying trigonometric identitieshow to verify trig identitieshow to verify trigonometric
Rewrite 12 sec2(x) 1 2 sec 2 ( x) as ( 1 sec(x))2 ( 1 sec ( x)) 2 Rewrite sec(x) sec ( x) in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by 1 cos(x) 1 cos ( x) Multiply cos(x) cos ( x) by 1 1Differentiate c and d, use the product rule to find v Then just use the product rule on u and v 0See the answer tan^2x−1/sec^2x=tan x−cotx/tan xcot x solution and steps please Expert Answer 100% (1 rating) Previous question Next question
Question 2502 prove that tanx (cotxtanx)=sec^2x i have no idea how to do this please help thank you Answer by Fombitz () ( Show Source ) You can put this solution on YOUR website!In Trigonemetry Laws and Identities, there are some rule that we will use to prove 1 / sec² (x) = cos² (x) * tan² (x) 1 = sec² (x) * sin² (x) cos² (x) = 1 * tan (x) = sin (x) / cos (x) We will prove from the Left Hand Side We know that sec²{eq}\frac{(\tan 2x)}{(1 \sec 2x)} = \tan x {/eq} Identities in Trigonometry The identities are trigonometric equations, in that, any value of the variable contained by the equation can make the
True or false the equation tan^2x1=sec^2x Get the answers you need, now!We get (tan(x))2 1 = (sec(x))2 1 = (sec(x))2 (tan(x))2 Now, we will see if 1 = (sec(x))2 (tan(x))2and 1 = (sec(x))2 (tan(x))2 canSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
Keep breaking it down until you find something you can work with Let u=sec^2 and v=tan^2 and if that's still too much at this stage Let a=sec b=sec c=tan d=tan Differentiate a and b, use the product rule to find u; A few hints 1 sec x = 1/(cos x) 2 (sin x)/(cos x) = tan x That should give you a good start$\begingroup$ so mu next step would be $2\ln((\tan x)) \cdot ln(tan)^2x\ cdot\frac{1}{sec^2x}$ $\endgroup$ – Sunny Jul 4 '15 at 07 Add a comment 5 Answers Active Oldest Votes 1 $\begingroup$ You make mistakes when applying the chain rule The function you are differentiating is
Verify (1tan^2x)/(1cot^2x) = 1sec^2x Answered by a verified Math Tutor or Teacher We use cookies to give you the best possible experience on our website By continuing to use this site you consent to the use of cookies on your device as described in our cookie policy unless you have disabled them$$ \tan^2x \sec^2x $$ $$ (\sin x / \cos x)^2 (x / \cos x)^2 $$ trigonometry Share Cite Follow edited Jan 17 '13 at 644 Paul 177k 3 3 gold badges 49 49 silver badges 77 77 bronze badges asked Jan 17 '13 at 639 sam sam 61 1 1 gold badge 3 3 silver badges 6 6 bronze badges $\endgroup$ 1 4Calculus 2, integral of (1tan^2x)/sec^2x, integral of cos(2x)
Hi Simplifying the following (sec^2x csc^2x) (tan^2x cot^2x) tan^2x = sec^2x 1 cot^2x = csc^2x 1 (sec^2x csc^2x) (sec^2x 1 csc^2x 1)= 2We know, $$\csc^2x\cot^2x=1=\sec^2x\tan^2x$$ Share Cite Follow answered Sep 30 '13 at 1430 lab bhattacharjee lab bhattacharjee 266k 17 17 gold badges 192 192 silver badges 304 304 bronze badges $\endgroup$ Add a comment 2 $\begingroup$Free trigonometric identities list trigonometric identities by request stepbystep
\(1\tan^2x = \sec^2x\) (the Pythagorean Theorem) If the integrand can be manipulated to separate a \(\sec^2x\) term with the remaining secant power even, or if a \(\sec x\tan x\) term can be separated with the remaining \(\tan x\) power even, the Pythagorean Theorem can be employed, leading to a simple substitutionAdal2762 adal2762 Mathematics Middle School answered True or false the equation tan^2x1=sec^2x 1 See answer adal2762 is waiting for your help Add your answer and earn points kudzordzifrancis kudzordzifrancisSec^2xtan^2x= 1 1cot^2x= csc^2x cot^2x= csc^2x1 csc^2xcot^2x= 1 YOU MIGHT ALSO LIKE 8 Basic Trig Identities 8 terms kovoquiz Algebra trig identities 11 terms clairebelfore Trigonomentry Formula 13 terms harini_chandrasekar Sin, Cos, Tan Equations 12 terms michellebarth OTHER SETS BY THIS CREATOR
Click here👆to get an answer to your question ️ If sec x sec^ 2x = 1 then the value of tan^ 8 tan^ 4 2tan^ 2x 1 will be equal to Trig Use the fundamental identities to simplify the expression cot beta sec beta I used 1tan^2u=secu since cot is the inverse of tan I flipped the tangent, then so it was 1 (1/tan)Math\int \frac{1\tan^2x}{1\tan^2x} \,dx/math math\int \frac{1\tan^2x}{\sec^2x} \,dx/math math\int \frac{1\tan^2x}{\frac{1}{\cos^2x}} \,dx/math math
Terms in this set (8) sin^2xcos^2x =1 tan^2x1 sec^2x 1cot^2x =csc^2xThe derivative of ax^ {n} is nax^ {n1} The derivative of a polynomial is the sum of the derivatives of its terms The derivative of a constant term is 0 The derivative of a x n is n a x n − 1 \sec (2x^ {1}1)\tan (2x^ {1}1)\times 2x^ {11} sec ( 2 x 1 − 1) tan ( 2 x 1 − 1) × 2 x 1 − 1 Simplify(sec x 1)(sec x 1) = tan^2 x
Answer to Solve the trigonometric equation on the interval \\parenthesis 0,2\\pi \\parenthesis \\tan(2x) 1 = \\sec(2x) By signing up, you'll get When trying to prove trig identities, it is often helpful to convert TAN functions into SIN/COS functions Proof Step 1 Start with the original equation to prove tan 2 x sin 2 x = (tan 2 x)(sin 2 x) Proof Step 2 Replace tan with sin/cos (sin 2 x/cos 2 x) sin 2 x = (sin 2 x/cos 2 x)(sin 2 x) Proof Step 3 Obtain a common denominator on left, simplify right (sin 2 x sin 2 x cos 2 x`1 tan^2x = 1tan^ 2 x` ANSWER The last line proves the identity`tan x(cot x tan x) = sec^2 x` Approved by eNotes Editorial Team Tushar Chandra Educator since 10 12,615 answers
Learn how to solve simplify trigonometric expressions problems step by step online Simplify the trigonometric expression 1/(sec(2x)tan(2x))(2sec(2x)*tan(2x)2sec(2x)^2) Multiply the fraction and term Factor the polynomial 2\sec\left(2x\right)\tan\left(2x\right)2\sec\left(2x\right)^2 by it's GCF 2\sec\left(2x\right) Ex 34, 8 Find the general solution of the equation sec2 2x = 1 – tan 2x sec2 2x = 1 – tan 2x 1 tan2 2x = 1 – tan2x tan2 2x tan2x = 1 – 1 tan2 2x tan2x = 0 tan 2x (tan2x 1) = 0 Hence We know that sec2 x = 1 tan2 x So, sec2 2x = 1 tan2 2x tan 2x = 0 taSeparate fractions Rewrite tan(x) tan ( x) in terms of sines and cosines Multiply by the reciprocal of the fraction to divide by sin(x) cos(x) sin ( x) cos ( x) Convert from cos(x) sin(x) cos ( x) sin ( x) to cot(x) cot ( x) Divide sec2(x) sec 2 ( x) by 1 1 Rewrite sec(x) sec ( x) in terms of sines and cosines
Solve for x tan (2x)=1 tan (2x) = 1 tan ( 2 x) = 1 Take the inverse tangent of both sides of the equation to extract x x from inside the tangent 2x = arctan(1) 2 x = arctan ( 1) The exact value of arctan(1) arctan ( 1) is π 4 π 4 2x = π 4 2 x = π 4 Divide each term by 2 Well, if we divide (cos(x))2 on both sides;2 x I started this by making sec 1/cos and using the double angle identity for that and it didn't work at all in any way ever Not sure why I can't do that, but something was wrong Anyways I looked at the solutions manual and they magic out 1 tan x tan 2 x = 1 tan
Question Tan^2x−1/sec^2x=tan X−cotx/tan Xcot X Solution And Steps Please This problem has been solved!Verify the Identity cot (x)^2 (sec (x)^21)=1 cot2 (x) (sec2 (x) − 1) = 1 cot 2 ( x) ( sec 2 ( x) 1) = 1 Start on the left side cot2(x)(sec2(x)−1) cot 2 ( x) ( sec 2 ( x) 1) Apply pythagorean identity cot2(x)tan2(x) cot 2 ( x) tan 2 ( x) Convert to sines and cosines Tap for more steps Write cot ( x) cot ( x) in sines and cosines Left hand side is cosx1/tan^2x and the right hand side is cosx/secx1 Click to expand \ Lcos(x) 1 tan2(x) = cos(x) sec(x) − 1 \L cos Since this is not actually an identity, you only need to find an xvalue for which the two sides are unequal, and you're done!
Note that `tan^2x1=sec^2x=1/(cos^2x) ` and `tan^2x=(sin^2x)/(cos^2x) ` Substituting we get `(tan^2x)/(1tan^2x)=((sin^2x)/(cos^2x))/(1/(cos^2x))=sin^2x ` as required Explanation Start with the well known pythagorean identity sin2x cos2x ≡ 1 This is readily derived directly from the definition of the basic trigonometric functions sin and cos and Pythagoras's Theorem Divide both side by cos2x and we get sin2x cos2x cos2x cos2x ≡ 1 cos2x ∴ tan2x 1 ≡ sec2xCot (x) = cot (x) sin ^2 (x) cos ^2 (x) = 1 tan ^2 (x) 1 = sec ^2 (x) cot ^2 (x) 1 = csc ^2 (x) sin (x y) = sin x cos y cos x sin y cos (x y) = cos x cosy sin x sin y tan (x y) = (tan x tan y) / (1 tan x tan y) sin (2x) = 2 sin x cos x cos (2x) = cos ^2 (x) sin ^2 (x) = 2 cos ^2 (x) 1 = 1 2 sin ^2 (x)
Found 2 solutions by ewatrrr, MathLover1 Answer by ewatrrr () ( Show Source ) You can put this solution on YOUR website! See the proof below We need tanx=sinx/cosx sin^2xcos^2x=1 secx=1/cosx Therefore, LHS=tan^2x1 =sin^2x/cos^2x1 =(sin^2xcos^2x)/cos^2x =1/cos^2x =sec^2x =RHS QED Trigonometry Science
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