Question

If sin-1x+sin-1y=2pi/3 then find the value of cos-1x +cos-1y

Answer 1

Answer:

Given: sin-1(x)+sin-1(y)=2π/3

Step-by-step explanation:

We know that,

cos-1(x) + sin-1(x) = π/2 ......eq.1

similarly, cos-1(y) + sin-1(y) = π/2 ......eq.2

Adding eq.1 and eq.2, we get

cos-1(x)+cos-1(y)+sin-1(x)+sin-1(y) = π/2+π/2

→ cos-1(x)+cos-1(y)+2π/3 = π

(putting the value of sin-1(x)+sin-1(y)=2π/3)

→cos-1(x)+cos-1(y) = π-(2π/3)

→cos-1(x)+cos-1(y) = (3π-2π)/3

→cos-1(x)+cos-1(y) = π/3 .......[Ans.]