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Question Number 46472 by peter frank last updated on 27/Oct/18

Answered by tanmay.chaudhury50@gmail.com last updated on 27/Oct/18

$${(asin\theta +bcos\theta )}^2=c^2$$$$a^2{sin}^2\theta +b^2{cos}^2\theta +2absin\theta cos\theta =c^2$$$$a^2(1-{cos}^2\theta )+b^2(1-{sin}^2\theta )+2absin\theta cos\theta =c^2$$$$a^2+b^2-c^2=a^2{cos}^2\theta +b^2{sin}^2\theta -2absin\theta cos\theta$$$$(a^2+b^2-c^2)={(acos\theta -bsin\theta )}^2$$$$so(acos\theta -bsin\theta )=\pm \sqrt{a^2+b^2-c^2}$$

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