Prove the following identity for any acute angle :

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Prove the following identity for any acute angle θ\theta : (i) Show that tan⁡θ tan⁡(90∘−θ)=1\tan\theta\,\tan(90^{\circ}-\theta)=1. (ii) Using part (i), prove that tan⁡θ tan⁡(90∘−θ)+cot⁡θ cot⁡(90∘−θ)=2\tan\theta\,\tan(90^{\circ}-\theta)+\cot\theta\,\cot(90^{\circ}-\theta)=2.

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