1.

Don't put silly amswers please​

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Answer:

LET theta = X

as x belongs to (- PIE, 0)

so x/2 belongs to ( - pie/2, 0)

x/2 lies in 4TH quadrant.

Consider

{tan}^{ - 1} \sqrt{ \frac{1 - cosx}{1 + cosx} } \\ = {tan}^{ -1 } \sqrt{ \frac{2 {sin}^{2} \frac{x}{2} }{2 {cos}^{2} \frac{x}{2} } } \\ = {tan}^{ - 1} |tan \frac{x}{2} | \\ = {tan}^{ - 1} ( - tan \frac{x}{2} ) \\ = - \frac{x}{2}


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