Answer the following questions related to complementary angles.

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

Problem

Answer the following questions related to complementary angles. (i) State the four standard complementary–angle identities for sin⁡\sin, cos⁡\cos, tan⁡\tan and cot⁡\cot. (ii) Using the identities stated in part (i), express each of the following only in terms of θ\theta. (a) cos⁡(90∘−θ)\cos(90^{\circ}-\theta) (b) tan⁡(90∘−θ)\tan(90^{\circ}-\theta) (c) cot⁡(90∘−θ)\cot(90^{\circ}-\theta) (iii) Complete the statement: If sin⁡(90∘−θ)=45\sin(90^{\circ}-\theta)=\dfrac{4}{5}, then cos⁡θ=          \cos\theta=\;\;\;\;\;.

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