Q. 515.0( 1 Vote )

If a cos θ – b sinθ = x and a sinθ + b cosθ = y that a2 + b2 = x2 + y2.

Answer :

Taking RHS =x2 + y2

Putting the values of x and y, we get


(a cos θ – b sin θ)2 + (a sin θ + b cos θ)2


= a2cos2θ + b2 sin2θ – 2ab cos θ sin θ + a2sin2θ + b2 cos2θ + 2ab cos θ sin θ


= a2 (cos2 θ + sin2 θ) + b2 (cos2 θ + sin2 θ)


= a2 + b2 [ cos2 θ + sin2 θ = 1]


=RHS


Hence Proved


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