Question

If `sin^-1  4/5 + cos^-1  12/13` = sin^–1α, then find the value of α.

Answer 1

Let `sin^-1  4/5` = A

and `cos^-1  12/13` = B

∴ sin A = `4/5`

and cos B = `12/13`

Consider sin(A + B) = sin A cos B + cos A sin B

= `4/5*12/13 + 3/5*5/13`

= `48/65 + 15/65`

= `48/65 + 15/65`

= `63/65`

∵ sin(A + B) = `63/65`

∴ A + B = `sin^-1  63/65`

i.e. `sin^-1  4/5 + cos^-1  12/13`

= `sin^-1  63/65`

= sin^–1α

∴ α = `63/65`