Let be an acute angle such that .

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Let θ\theta be an acute angle such that sin⁡θ=513\sin\theta=\dfrac{5}{13}. (i) Find cos⁡θ\cos\theta and tan⁡θ\tan\theta. (ii) Simplify the expression S=sec⁡θ (1−sin⁡2θ)+tan⁡2θS=\sec\theta\,(1-\sin^2\theta)+\tan^2\theta and hence calculate its numerical value.

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