Question

if sin-1 x/5+cosec-1 5/4=π/2 then thd value of x is ​

Answer 1

Answer:

x = 3.

Step-by-step explanation:

It is known that, (3,4,5) are pythagorean triplets.   ---------------(1)

Now,   $sin^{-1}(\frac{x}{5}) +cosec^{-1}(\frac{5}{4} )=\frac{\pi}{2}$

     =>  $sin^{-1}(\frac{x}{5} )+sin^{-1}(\frac{4}{5} )=\frac{\pi}{2}$

     =>  $sin^{-1}(\frac{x}{5} )+cos^{-1}(\frac{3}{5} )= \frac{\pi}{2}$       [From (1)]

And also,  $sin^{-1}A+cos^{-1}A = \frac{\pi}{2}$

Therefore,   $\frac{x}{5}= \frac{3}{5}$

            =>  x = 3.