Question

if sin(sin inverse 1/5+cos inverse x) = 1, find x

Answer 1

Hey there !!!!

sin(sin⁻¹1/5+cos⁻¹x)=1

sin⁻¹1/5+cos⁻¹x=sin⁻¹1

But sinπ/2=1
 
       sin⁻¹1=π/2
So,

  sin⁻¹1/5+cos⁻¹x=π/2-------------------Equation 1

In inverse trigonometry 

    sin⁻¹t+cos⁻¹t=π/2

So, equation 1 follows the above identity

So, sin⁻¹ 1/5+cos⁻¹x=π/2

Therefore value of x will be 1/5.