Starting with the identity

MATHEMATICS · Single correct · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Starting with the identity 1+tan⁡2x=sec⁡2x1+\tan^2 x = \sec^2 x, a student performs the following two steps: (i) divides both sides by tan⁡2x\tan^2 x, (ii) replaces 1tan⁡x\dfrac{1}{\tan x} with cot⁡x\cot x. Which of the following identities should the student obtain? (a) cot⁡2x−1=csc⁡2x\cot^2 x - 1 = \csc^2 x (b) cot⁡2x+1=sec⁡2x\cot^2 x + 1 = \sec^2 x (c) 1+cot⁡2x=csc⁡2x1+\cot^2 x = \csc^2 x (d) 1+cot⁡2x=csc⁡x1+\cot^2 x = \csc x

Related theory

Browse the problem library