IIT JEE , AIEEE Forum - Chemistry , Inorganic Chemistry - If cosec-1 x=2 cot-1 7 +cos-1 3/5,then the value of x is :

sunilseth558

If cosec-1 x=2 cot-1 7 +cos-1 3/5,then the value of x is :

sriram.a

$tan^{-1}(\frac{1}{\sqrt{x^2-1}})=2tan^{-1}(\frac{1}{7})+tan^{-1}(\frac{4}{3})$

$tan^{-1}(\frac{2/7}{48/49})+tan^{-1}(4/3)$

$=tan^{-1}(\frac{7/24+4/3}{1-(7/24)(4/3)}$

$=tan^{-1}(117/44)$

$\frac{1}{\sqrt{x^2-1}}=117/44$

simplfy, x=125/117