Answer the questions that follow

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

Problem

Answer the questions that follow, giving clear reasons. (i) Explain why sin⁡(90∘−θ)=cos⁡θ\sin(90^\circ-\theta)=\cos\theta and verify this relation numerically for θ=30∘\theta=30^\circ. (ii) Using the relation in part (i), show that sin⁡30∘+cos⁡60∘=1\sin30^\circ+\cos60^\circ=1. (iii) Without carrying out any calculation, state whether sin⁡45∘−cos⁡45∘\sin45^\circ-\cos45^\circ is positive, negative, or zero, and justify your answer briefly.

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