Question

if sin (sin-1 1/5+cos-1 x) =1 find the value of x?

Answer 1

Given that:

$\red{ \sin ({sin {}^{ - 1} \frac{1}{5} + \cos {}^{ - 1} x)} = 1}$

☘️SolutiOn:

$\sin( \sin {}^{ - 1} \frac{1}{5} + \cos {}^{ - 1} x) = \sin \frac{\pi}{2} \\ \sin {}^{ - 1} \frac{1}{5} + \cos {}^{ - 1}x = \frac{\pi}{2} \\ \sin {}^{ - 1} \frac{1}{5} = \frac{\pi}{2} - \cos {}^{ - 1} x \\ \sin {}^{ - 1} \frac{1}{5} = \sin {}^{ - 1} x \\ \green{ \boxed{x = \frac{1}{5} }}$