Question

If `sin^-1  3/5 + cos^-1  12/13 = sin^-1 P`, then P is equal to ______ 

Options

• `54/65`

• `56/65`

• `61/65`

• `60/65`

Answer 1

If `sin^-1  3/5 + cos^-1  12/13 = sin^-1 P`, then P is equal to `underline(56/65)`.

Explanation:

`sin^-1  3/5 + cos^-1  12/13`

= `tan^-1  (3/4) + tan^-1  (5/12)`

= `tan^-1  ((3/4 + 5/12)/(1 - 3/4 . 5/12))` 

= `tan^-1 (14/12 xx 48/33)`

= `tan^-1  (56/33) = sin^-1 (56/65)`

∴ P = `56/65`