Question

If 2cosa-sina=x,cosa-3sina=y prove that 2x 2 +y 2 -2xy=5

Answer 1

2cosa-sina=x   
cosa-3sina=y
x²=4cos²a-4sinacosa+sin²a
y²=cos²a-6sinacosa+9sin²a
xy=(2cosa-sina)(cosa-3sina)
    =2cos²a-sinacosa-6sinacosa+3sin²a
    =2cos²a-7sinacosa+3sin²a
∴, 2x²+y²-2xy
=8cos²a-8sinacosa+2sin²a+cos²a-6sinacosa+9sin²a-4cos²a+14sinacosa-6sin²a
=5cos²a+5sin²a
=5(sin²a+cos²a)
=5 (Proved)

Answer 2

Answer:

Here is your answer mate.