Solveeit Logo
Login

Question

Question: If \(\tanh^{2}x = \tan^{2}\theta,\) then \({\cos h}2x\) is equal to...

If tanh⁡2x=tan⁡2θ,\tanh^{2}x = \tan^{2}\theta, then cos⁡h2x{\cos h}2x is equal to

A

−sin⁡2θ- \sin 2\theta

B

sec⁡2θ\sec 2\theta

C

cos⁡3θ\cos 3\theta

D

cos⁡2θ\cos 2\theta

Answer

sec⁡2θ\sec 2\theta

Explanation

Solution

cos⁡h2x=1+tan⁡h2x1−tan⁡h2x=1+tan⁡2θ1−tan⁡2θ\cos h2x = \frac{1 + \tan h^{2}x}{1 - \tan h^{2}x} = \frac{1 + \tan^{2}\theta}{1 - \tan^{2}\theta}

=11−tan⁡2θ1+tan⁡2θ=1cos⁡2θ=sec⁡2θ\frac{1}{\frac{1 - \tan^{2}\theta}{1 + \tan^{2}\theta}} = \frac{1}{\cos 2\theta} = \sec 2\theta