Question

If 3 cot theta= 2, find the value of 2sin theta -3cos theta /2sin theta +3cos theta

Answer 1

0

Explanation:

Using the trigonometric identity

cotx =
`(cosx)/(sinx)`

Given

3cotθ = 2 , then

3
`(coso)/(sino)` = 2 ( multiply both sides by sinθ )

3cosθ = 2sinθ ( subtract 3cosθ from both sides )

2sinθ - 3cosθ = 0

Thus

`(2sin0-3cos0)/(2sin0+3cos0)`

=
`(0)/(2sin0+3cos0)`

= 0