For any acute angle

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

For any acute angle θ\theta, define H(θ)=(sec⁡2θ−tan⁡2θ)+[csc⁡2(90∘−θ)−cot⁡2(90∘−θ)].H(\theta)=\bigl(\sec^{2}\theta-\tan^{2}\theta\bigr)+\bigl[\csc^{2}(90^{\circ}-\theta)-\cot^{2}(90^{\circ}-\theta)\bigr]. Calculate the value of H(θ)H(\theta) when θ=42∘\theta=42^{\circ} without using a calculator, showing all working.

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