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 taProve tan^{2}(x) (1cot^{2}x) = sec^{2}x en Related Symbolab blog posts High School Math Solutions – Trigonometry Calculator, Trig Identities In a previous post, we talked about trig simplification Trig identities are very similar to this concept An identityProve that 1 tan^2 x = sec^2 x We know that tan x = sin x/cos x and so tan 2 x = sin 2 x/cos 2 x We also know that sin 2 x cos 2 x = 1 because this is a Pythagorean identity We can rewrite the left hand side as (cos 2 x sin 2 x)/cos 2 x because 1 can be rewritten as cos 2 x/cos 2 x
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1 tan^2x=sec^2x proof
1 tan^2x=sec^2x proof- 1tanx*tan2x = sec 2x LS =1 (sin x/cos x)(sin 2x/ cos 2x) =1 (sin x/cos x)(2sin x* cos x)/ cos 2x) =12sin^2(x)/(cos 2x) ={cos(2x) 2sin^2(x)}/cos (2x) See explanation Starting from cos^2(x) sin^2(x) = 1 Divide both sides by cos^2(x) to get cos^2(x)/cos^2(x) sin^2(x)/cos^2(x) = 1/cos^2(x) which simplifies to
Answered 3 1 Tanx Tan 2x Sec 2x S Bartleby
How to prove $\cot ^2x\sec ^2x=\tan ^2x\csc ^2x$?Answer (1 of 3) Well, using pythagarian identities we know that cos^2 u sin^2 u= tan^2 u ( and by deviding both sides by Cos^u) 1 tan^2 u= sec^2 u To Solve 2sec^2 x 1=12tan^2 x * Add 1 to both sides 2sec^2 x =22tan^2 x * Factor out the 2 sec^2 x= 1 tan^2 x * Use the Pythag Ide Prove the following identities $$(\sec^2 x \tan^2x)(\csc^2 x \cot^2x) = 1 2 \sec^2x \csc^2 x \tag i$$ $$\frac{\cos x}{1\tan x} \frac{\sin x}{1\cot x} = \sin x \cos x \tag {ii}$$ For $(\mathrm i)$ , I initially tried simplifying what was in the 2 brackets but ended up getting 1 1
Free trigonometry calculator calculate trignometric equations, prove identities and evaluate functions stepbystep This website uses cookies to ensure you get the best experience By using this website, you agree to our Cookie PolicyAsk Question Asked 8 years ago Active 6 years, 2 months ago Viewed 10k times Do you know, $\cot^2(x) 1 = \csc^2(x)$ and $\tan^2(x) 1 = \sec^2(x)$ So, $\cot ^2x\sec ^2x=\csc^2(x)1\tan^2(x) 1=\tan^2(x)\csc^2(x)$ Thus, we end up with $\cot ^2x\sec ^2x=\tan^2(x)\csc^2(x)$Tanx = t Sec^2 x dx= dt So now it is, 1/ (1t)^2 dt This integral is given by 1/1t and t= tanx So, it is cosx/cosx sinx tanx = t Sec^2 x dx= dt So now it is, 1/ (1t)^2 dt This integral is given by 1/1t and t= tanx So, it is cosx/cosx sinx Integral of the function \frac {\cos ^2 x} {1\tan x}
We are asked to prove {eq}(\sec x 1)(\sec x 1) = \tan^2x {/eq} When proving an identity, we only work with one side usually the messier one In this problem, we will work with the left side Using the following tan(x) = sin(x)/cos(x) cos^2(x)sin^2(x) = 1 sec(x) = 1/cos(x) for cos(x)!=0, we have 1tan^2(x) = cos^2(x)/cos^2(x) (sin(x)/cos(x))^2 =cos^2(x rhs = sec2x tan2x = (a million/ cos2x) (sin2x/cos 2x) =( a million sin 2x) / cos 2x a million sin2x = a million 2sinx cosx = cos^ 2 x sin^2 x 2 sin x
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