Question

sin(cot inverse 1/2)=tan (cos inverse X) then the value of X ​

Answer 1

Answer:

$\sin( \cot {}^{ - 1} ( \frac{1}{2} ) ) = \sin( \sin {}^{ - 1} ( \frac{2}{ \sqrt{ {2}^{2} + 1} } ) ) = \frac{2}{ \sqrt{5} }$

Now

$\tan( \cos {}^{ - 1} (x) ) = \frac{2}{ \sqrt{5} } \\ \cos {}^{ - 1} (x) = \tan {}^{ - 1} ( \frac{2}{ \sqrt{5} } ) \\ \cos {}^{ - 1} (x) = \cos {}^{ - 1} ( \frac{ \sqrt{5} }{ \sqrt{5 + {2}^{2} } } ) = \cos^-( \frac{ \sqrt{5} }{3} ) \\ x = \frac{ \sqrt{5} }{3}$