Two complementary angles are considered in this problem.

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

Problem

Two complementary angles are considered in this problem. (i) Prove that sin⁡2θ+sin⁡2(90∘−θ)=1\sin^{2}\theta+\sin^{2}(90^{\circ}-\theta)=1 for every acute angle θ\theta. (ii) If sin⁡θ=45\sin\theta=\dfrac{4}{5} for an acute θ\theta, find sin⁡(90∘−θ)\sin(90^{\circ}-\theta) and verify the result obtained in part (i) numerically.

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