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

1 Answer
Jun 20, 2018

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