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Math Help - Verify Identity

  1. #1
    Junior Member
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    Verify Identity

    I having trouble on verify identitys can somone please explain how to do these?

    *0=theta*

    a. Tan0sin0+cos0=sec0

    b. sec^(4)x-tan^(4)x=sec^(2)x+tan^(2)x
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  2. #2
    Senior Member Twig's Avatar
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    A)

     tan(\theta)\cdot sin(\theta) + cos(\theta)=\frac{1}{cos(\theta)}

     \frac{sin^{2}(\theta)}{cos(\theta)}+cos(\theta)=\f  rac{1}{cos(\theta)}

     sin^{2}(\theta) + cos^{2}(\theta) = \frac{cos(\theta)}{cos(\theta)} = \mbox{ Trig. identity } = 1
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  3. #3
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    Hello, goldenroll!

    a)\;\;\tan\theta\sin\theta +\cos\theta \:=\:\sec\theta
    \tan\theta\sin\theta + \cos\theta \:=\:\frac{\sin\theta}{\cos\theta}\cdot\sin\theta + \cos\theta \;=\;\frac{\overbrace{\sin^2\!\theta + \cos^2\!\theta}^{\text{This is 1}}}{\cos\theta} \;=\;\frac{1}{\cos x} \;=\;\sec x



    b)\;\;\sec^4\!x-\tan^4\!x \;=\;\sec^2\!x+\tan^2\!x
    \sec^4\!x - \tan^4\!x \;=\;\overbrace{(\sec^2\!x-\tan^2\!x)}^{\text{This is 1}}(\sec^2\!x + \tan^2\!x) \;=\; \sec^2\!x + \tan^2\!x

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