1i tried it by converting it in its basic form and was last left with the expression 2-cos2x+sinxcos2x+sinx=7sinxcosx
2 Answers
341We may rewrite the expression as \sin x + \cos x + \frac{1}{\sin x \cos x} + \frac{\sin x + \cos x}{\sin x \cos x} = 7
Let \sin x + \cos x =t
Then we have t+\frac{2(t+1)}{t^2-1} = t + \frac{2}{t-1} = 7 which gives one admissible solution t = 4 -\sqrt 7
Hence x satisfies \sin x + \cos x = \sqrt 2 \sin \left(x + \frac{\pi}{4} \right) = 4 - \sqrt 7 which can be solved to find x
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