If-sin-1-x-5-cosec-1-5-4-pi-2-then-x-

Question Number 96845 by DELETED last updated on 05/Jun/20

If \sin^{- 1} \frac{x}{5} + {cosec}^{- 1} \frac{5}{4} = \frac{π}{2}, then x =

Answered by Sourav mridha last updated on 05/Jun/20

\Rightarrow \sin^{- 1} (\frac{x}{5}) = \cos^{- 1} (\frac{4}{5}) = \sin^{- 1} \frac{3}{5}

\Rightarrow x = 3

Answered by 1549442205 last updated on 05/Jun/20

putting \sin^{- 1} \frac{x}{5} = α, {cosec}^{- 1} \frac{5}{4} = β

\Rightarrow \sin α = \frac{x}{5}, \frac{1}{\sin β} = \frac{5}{4}, α + β = \frac{π}{2}

\Rightarrow \sin β = \frac{4}{5} = \sin (\frac{π}{2} - α) = \cos α

\Rightarrow 1 = \cos^{2} α + \sin^{2} α = \frac{16}{25} + \frac{x^{2}}{25}

\Rightarrow x^{2} = 9 \Rightarrow x = 3