Question

3 sin theta+5 cos theta=5,then the value of 5 sin theta - 3 cos theta is?

Answer 1

Answer is `+- 3`

Explanation:

Let me take theta=α(I can't find the symbol)
`3sinα+5cosα=5`
Squaring both sides
`9(sinα)^2 +25(cosα)^2+30*sinα*cosα=25`
`9-9(cosα)^2 + 25 -25(sinα)^2+30*sinα*cosα=25`
Cutting 25 both sides and multiplying -1 both sides we get
`9(cosα)^2+25(sinα)^2-30*cosα*sinα=9`

`(5sinα-3cosα)^2=3^2`
`5sinα-3cosα=+3 or -3`