Answer the following questions related to the constant nature of certain…

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

Problem

Answer the following questions related to the constant nature of certain trigonometric combinations. (i) Without substituting any numerical values, explain why sin⁡2θ+cos⁡2θ=1\sin^2 \theta + \cos^2 \theta = 1 for every acute angle θ\theta in a right-angled triangle. (ii) Using your reasoning from part (i), state whether (sin⁡230∘+cos⁡260∘)(\sin^2 30^\circ + \cos^2 60^\circ) is equal to, less than, or greater than 1. Give a brief justification. (iii) Calculate the exact numerical value of (sin⁡230∘+cos⁡260∘)(\sin^2 30^\circ + \cos^2 60^\circ) to confirm your answer in part (ii).

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