Question

sin⁻¹x-sin⁻y=2π/3 then (cos⁻¹x+cos⁻¹y) find the value​

Answer 1

we know, a very important formula,

\qquad\bf{sin^{-1}P+cos^{-1}P=\frac{\pi}{2}}sin

−1

P+cos

−1

P=

2

π

where |P| ≤ 1

so, sin^-1x + cos^-1x = π/2 .......(1)

and sin^-1y + cos^-1y = π/2 ...........(2)

now Given, sin^-1x + sin^-1y = 2π/3

π/2 - cos^-1x + π/2 - cos^-1y = 2π/3 [from equations (1) and (2), ]

π - [cos^-1x + cos^-1y] = 2π/3

π - 2π/3 = cos^-1x + cos^-1y

cos^-1x + cos^-1y = π/3