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

1 Answer
IZUkuABA
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#

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