Question

If 2cos theta - sin theta = x and cos theta - 3sin theta =y . Prove that 2x^2+y^2 - 2xy=5

Answer 1

The answer is in photograph

Answer 2

HELLO DEAR,


GIVEN:-


2cos theta - sin theta = x


and


(cosθ - 3 sinθ) = y


PUT THE VALUES OF X AND Y IN

2x2 + y2 − 2xy (LHS)


= 2(2 cosθ − sinθ)2 + (cosθ − 3 sinθ)2 

− 2(2 cosθ − sinθ)(cosθ − 3 sinθ)


= 2(4cos2θ − 4cosθ sinθ + sin2θ)


+ (cos2θ − 6cosθ sinθ + 9sin2θ)


− 2(2cos2θ − 7cosθ sinθ + 3sin2θ)


= 8cos2θ − 8cosθ sinθ + 2sin2θ + cos2θ



− 6cosθ sinθ + 9sin2θ − 4cos2θ



+ 14cosθ sinθ − 6sin2θ


= 5cos2θ + 5sin2θ


= 5(cos2θ + sin2θ)


= 5(1) = 5        (Since cos2θ + sin2θ = 1)


= RHS


. I HOPE ITS HELP YOU DEAR,

THANKS