Question

If y = tan^-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.

Options

• `- 3/2`

• `- 1/2`

• `3/2`

• `1/2`

Answer 1

If y = tan^-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = `underline(3/2)`.

Explanation:

y = tan^-1 `((1 - cos 3x)/(sin 3x))`

`=> "y" = tan^-1((2 sin^2((3x)/2))/(2 sin  (3x)/2 cos  (3x)/2))`

`=> "y" = tan^-1 ((sin ((3x)/2))/(cos((3x)/2)))`

`=> "y" = tan^-1 (tan  (3x)/2)`

`=>"y" = (3x)/2`

`therefore "dy"/"dx" = 3/2`