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Math Help - Another question proving that a trig equation follows from another given trig equatio

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    Another question proving that a trig equation follows from another given trig equatio

    a\cos\theta - b\sin\theta=c

    Then show that a\sin\theta + b\cos\theta=\sqrt{a^2+b^2-c^2}
    Last edited by mr fantastic; July 24th 2009 at 04:38 AM.
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    Hello,

    Square the first equation :
    a^2\cos^2\theta+b^2\sin^2\theta-2ab\cos\theta\sin\theta=c^2
    Thus 2ab\cos\theta\sin\theta={\color{red}a^2\cos^2\thet  a+b^2\sin^2\theta-c^2}

    Then (a\sin\theta+b\cos\theta)^2=a^2\sin^2\theta+b^2\co  s^2\theta+2ab\cos\theta\sin\theta
    =a^2\sin^2\theta+b^2\cos^2\theta+{\color{red}a^2\c  os^2\theta+b^2\sin^2\theta-c^2}
    =a^2(\cos^2\theta+\sin^2\theta)+b^2(\cos^2\theta+\  sin^2\theta)-c^2

    And this gives you the result, using the identity \cos^2\theta+\sin^2\theta=1
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