if x=asinθ+bcosθ and y=acosθ+bsinθ then prove that x²+y²=a²+b²
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There is a mistake in this question.
I.e y= a cos theta - b sin theta
It will be solved as:
Take x^2 + y^2
=a^2sin^2theta+b^2cos^2theta+2ab sin theta cos theta + a^2cos^2theta + b^2sin^2theta-2ab Sin theta cos theta
=a^2(sin^2theta + cos^2theta) + b^2(cos^2theta + sin^2theta)
=a^2(1) + b^2(1)
=a^2 + b^2= rha
I.e y= a cos theta - b sin theta
It will be solved as:
Take x^2 + y^2
=a^2sin^2theta+b^2cos^2theta+2ab sin theta cos theta + a^2cos^2theta + b^2sin^2theta-2ab Sin theta cos theta
=a^2(sin^2theta + cos^2theta) + b^2(cos^2theta + sin^2theta)
=a^2(1) + b^2(1)
=a^2 + b^2= rha
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