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If x=asin~+bcos~ Y=acos-bsin~ Prove that x2+y2=a2+b2 …

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If x=asin~+bcos~ Y=acos-bsin~ Prove that x2+y2=a2+b2 (~ symbolises teta and 2 is square of a;b;x;y)

Posted by Srihari Addala 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

According to the question,
{tex}x^2 + y^2 = (asin\theta + bcos\theta)^2 + (acos\theta - bsin\theta)^2{/tex}

^{= {tex}a^2sin^2\theta+b^2cos^2\theta+2abcos\theta sin\theta+a^2cos^2\theta+b^2sin^\theta -2ab sin\theta cos\theta{/tex}}
= a²(sin²{tex}\theta{/tex} + cos²{tex}\theta{/tex}) + b²(cos²{tex}\theta{/tex} + sin²{tex}\theta{/tex})
{tex}= a^2 + b^2{/tex} [{tex}\because{/tex} sin²{tex}\theta{/tex} + cos²{tex}\theta{/tex} = 1].
{tex}\therefore{/tex} {tex}x^2 + y^2 = a^2 + b^2.{/tex}

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