Question

sin inverse 2x root 1 - x square is equal to 2 cos inverse X​

Answer 1

Step-by-step explanation:

             Let 2cos⁻¹(x) = A

cos⁻¹(x) = A/2      ⇒ cos(A/2) = x  

                So, sin(A/2) = √1 - x²

sinA = sin2(A/2) = 2sin(A/2)cos(A/2)

               = 2(√1 - x²)(x)

Hence,  

sinA = sin[2cos⁻¹(x)] = 2x√1 - x²

      ⇒ sin⁻¹(2x√1 - x²) = 2cos⁻¹(x)

       Proved.

Answer 2

Answer:

Step-by-step explanation:

             Let 2cos⁻¹(x) = A

cos⁻¹(x) = A/2      ⇒ cos(A/2) = x  

                So, sin(A/2) = √1 - x²

sinA = sin2(A/2) = 2sin(A/2)cos(A/2)

               = 2(√1 - x²)(x)

Hence,  

sinA = sin[2cos⁻¹(x)] = 2x√1 - x²

      ⇒ sin⁻¹(2x√1 - x²) = 2cos⁻¹(x)

       Proved.