Question

Solve: `sin^-1  5/x + sin^-1  12/x = pi/2`

Answer 1

`sin^-1  5/x = pi/2 - sin^1  12/x`

`pi/2 - (cos^-1  5/x) = pi/2 - sin^-1  12/x`

`cos^-1  5/x = sin^-1  12/x`

cos θ = `5/x`

sin θ = `12/x`

`sin^2theta + cos^2theta` = 1

`(5/x)^2 + (12/x)^2` = 1

`25/x + 144/x^2` = 1

`169/x^2` = 1

x² = 169

⇒ x = `+- 13`