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Math Help - 2 trig problems pls help...

  1. #1
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    Talking 2 trig problems pls help...

    1) show that cosec \theta/(cosec \theta-sin \theta)=sec^2 \theta

    2) solve: sin3 \thetacos2 \theta=sin2 \thetacos3 \theta for 0< \theta<2 \pi

    thanks in advance
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  2. #2
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    Hello, snowball!

    1) Show that: . \frac{\csc\theta}{\csc\theta -\sin\theta} \:=\:\sec^2\!\theta

    On the left side, multiply top and bottom by \sin\theta

    . . \frac{\sin\theta(\csc\theta)}{\sin\theta(\csc\thet  a-\sin\theta)} \:=\:\frac{1}{1-\sin^2\!\theta} \;=\;\frac{1}{\cos^2\!\theta} \;=\;\sec^2\!\theta




    2) Solve: . \sin3\theta\cos2\theta \:=\:\sin2\theta \cos3\theta,\;\;\text{ for }0 \leq \theta < 2\pi

    \text{We have: }\;\underbrace{\sin3\theta\cos2\theta - \sin2\theta\cos3\theta} \;=\;0

    . . . . . . . . . . . \overbrace{\sin(3\theta-2\theta)} \;=\;0

    . . . . . . . . . . . . \sin\theta \;=\;0

    Therefore:. \theta \;=\;0.\:\pi

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