(a) If $u=\log (\tan x+\tan y+\tan z)$ prove that $\sin 2 x \frac{\partial u}{\partial x}+\sin 2 y \frac{\partial u}{\partial y}+\sin 2 z \frac{\partial u}{\partial z}=2$.

Explanation

The given expression can be simplified using the identity $\sin 2a = 2 \sin a \cos a$ and the chain rule. The final answer is obtained by substituting the values of $\frac{\partial u}{\partial x}$, $\frac{\partial u}{\partial y}$, and $\frac{\partial u}{\partial z}$ in the given expression.

(a) If $u=\log (\tan x+\tan y+\tan z)$ prove that $\sin 2 x \frac{\partial u}{\partial x}+\sin 2 y \frac{\partial u}{\partial y}+\sin 2 z \frac{\partial u}{\partial z}=2$.

Explanation

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