Two Fractions That Collapse

Introduction to Trigonometry

Two Fractions That Collapse

CBSE Class 10 · Solve it one decision at a time. A wrong pick earns a nudge, never the answer.

Step 1 of 4

The problem

For 0∘<θ<90∘,0^\circ < \theta < 90^\circ, prove that tan⁡2θsec⁡θ−1+cot⁡2θcosec⁡θ+1=sec⁡θ+cosec⁡θ.\dfrac{\tan^2\theta}{\sec\theta - 1} + \dfrac{\cot^2\theta}{\operatorname{cosec}\theta + 1} = \sec\theta + \operatorname{cosec}\theta.

Step 1 · Your move

Which expression in sec⁡θ\sec\theta equals tan⁡2θ\tan^2\theta?

tan⁡2θsec⁡θ−1+cot⁡2θcosec⁡θ+1\dfrac{\tan^2\theta}{\sec\theta - 1} + \dfrac{\cot^2\theta}{\operatorname{cosec}\theta + 1}
Helpful?