prob

We 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