Question

If sin⁻¹ x + sin⁻¹ y = 2 , then the value of cos⁻¹ x + cos⁻¹ y is _
(a) 2π/3 (b) π/3 (c) π/2 (d) π

Answer 1

Explanation:

If sin⁻¹ x - cos⁻¹ x = π/6...eq1

, then to find the value x,we must convert the entire equation into one inverse triginomertic function,by using formula's of inverse triginomertry.

As we know that

sin⁻¹ x + cos⁻¹ x =π/2

so sin⁻¹ x =π/2-cos⁻¹ x

put this value to sin⁻¹ x into eq1

π/2-cos⁻¹ x-cos⁻¹ x=π/6

-2cos⁻¹ x =π/6-π/2

2cos⁻¹ x=2π/6

cos⁻¹ x=π/6

take cos both sides

cos(cos⁻¹ x)=cos(π/6)

x=√3/2