Question

Prove that
1/(sec x - 1) + 1/(sec x + 1) is equal to
2cos x × cosec^2 x

Answer 1

Explanation:

`1+tan^2\theta=sec^2\theta\\tan^2\theta=sec^2\theta -1 \\tan^2\theta=(sec\theta-1)(sec\theta+1)\\\implies (1)/(sec\theta-1) =(sec\theta+1)/(tan^2\theta) \\\\and \quad (1)/(sec\theta+1) =(sec\theta-1)/(tan^2\theta) \\\\ (1)/(sec\theta-1) + (1)/(sec\theta+1) = (sec\theta+1)/(tan^2\theta) + (sec\theta-1)/(tan^2\theta)\\\\=(2sec\theta)/(tan^2\theta)\\\\=(2cos^2\theta)/(cos\theta.sin^2\theta)\\\\\\=2cos\theta.cosec^2\theta`