Question

$\red\sf\ {tan}^{ - 1} ( \sqrt{ \frac{1 - cos \: x}{1 + cos \: x} }) \: \: \: \ddot \smile$
solve fast​

Answer 1

Answer:

$\boxed{\tt\huge \implies: \frac{x}{2} }$

Step-by-step explanation:

$\sf\huge {tan}^{ - 1} ( \sqrt{ \frac{1 - cos \: x}{1 + cos \: x} }) \\ \\ \tt\ \implies: {tan}^{ - 1} \: \: \sqrt{ \frac{ \cancel2 {sin}^{2} \frac{x}{2} }{ \cancel2 {cos}^{2} \frac{x}{2} } }\\ \\\tt\ \implies: {tan}^{ - 1} \: \: \frac{sin \frac{x}{2} }{cos \frac{x}{2} } \\ \\ \tt\ \implies: {tan}^{ - 1} tan \: \frac{x}{2} \\ \\ \boxed{\tt\huge \implies: \frac{x}{2} }$

Answer 2

Step-by-step explanation:

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