Question

If sin(x + y) + cos(x + y) = sin`[cos^-1 (1/3)],` then `"dy"/"dx"` = ?

Options

• 1

• - 1

• `1/2`

• 0

Answer 1

- 1

Explanation:

We have,

sin(x + y) + cos(x + y) = sin`[cos^-1 (1/3)]`

on differentiating w.r.t. 'x', we get

cos(x + y)`(1 + "dy"/"dx") - sin(x - y) (1 + "dy"/"dx")` = 0

`(1 + "dy"/"dx")`(cos(x + y) - sin(x + y)) = 0

`=> 1 + "dy"/"dx"` = 0

`=> "dy"/"dx" = - 1`