Answer the following for .

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Answer the following for 0<x<π20<x<\frac{\pi}{2}. (a) Show that log⁡9(cos⁡2x+2)=log⁡3cos⁡2x+2\log_9(\cos2x+2)=\log_3\sqrt{\cos2x+2}. (b) Hence or otherwise solve log⁡3(2sin⁡x)=log⁡9(cos⁡2x+2)\log_3(2\sin x)=\log_9(\cos2x+2) for 0<x<π20<x<\frac{\pi}{2}.

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