A right-angled triangle has one acute angle

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

Problem

A right-angled triangle has one acute angle θ\theta. Answer the following questions based on this information. (i) Define complementary angles in the context of a right-angled triangle. (ii) Prove that sin⁡(90∘−θ)=cos⁡θ\sin(90^{\circ}-\theta)=\cos\theta by using the definitions of the trigonometric ratios for the two acute angles of the triangle. (iii) With the help of the same triangle, explain why tan⁡(90∘−θ)=cot⁡θ\tan(90^{\circ}-\theta)=\cot\theta. State each step of your reasoning clearly.

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