Let G=sin⁡θ sec⁡θ1+tan⁡θ+cos⁡θ csc⁡θ1+cot⁡θ,G = \frac{\sin\theta\,\sec\theta}{1+\tan\theta}+\frac{\cos\theta\,\csc\theta}{1+\cot\theta},…

Mathematics

Problem

Let G=sin⁡θ sec⁡θ1+tan⁡θ+cos⁡θ csc⁡θ1+cot⁡θ,G = \frac{\sin\theta\,\sec\theta}{1+\tan\theta}+\frac{\cos\theta\,\csc\theta}{1+\cot\theta}, where θ\theta is an acute angle. (i) Simplify the first term of GG. (ii) Simplify the second term of GG. (iii) Hence show that G=1G = 1.

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