If , where and are positive acute angles, show that…

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

If 1cos⁡αcos⁡β+tan⁡αtan⁡β=tan⁡γ\frac{1}{\cos\alpha\cos\beta}+\tan\alpha\tan\beta=\tan\gamma, where 0<γ<π20<\gamma<\frac{\pi}{2} and α,β\alpha,\beta are positive acute angles, show that π4<γ<π2\frac{\pi}{4}<\gamma<\frac{\pi}{2}.

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