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Math Help - How can I verify the identity when it doesn't match?

  1. #1
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    How can I verify the identity when it doesn't match?

    The questions is
    Verify the identity: sec(x+y)=secxsecy/1-tanxtany

    I have a list of identities but it doesn't fully match either of them. Since sec is the reciprocal of sin, can I used this: sin(x-y)=sinxcosy-cosxsiny? If so, what would take the place of cos? csc? Thanks
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  2. #2
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    Quote Originally Posted by captaintoast87 View Post

    Since sec is the reciprocal of sin
    ... of cos.
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    ... of cos.
    ...of course !
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  4. #4
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    Hello, captaintoast87!

    Verify the identity: . \sec(x+y) \:=\:\frac{\sec x\sec y}{1-\tan x\tan y}

    The right side is: . \frac{\dfrac{1}{\cos x}\cdot\dfrac{1}{\cos y}} {1 - \dfrac{\sin x}{\cos x}\cdot\dfrac{\sin y}{\cos y}}


    Multiply top and bottom by \cos x\cos y

    . . \frac{\cos x\cos y\left(\dfrac{1}{\cos x}\cdot\dfrac{1}{\cos y}\right)} {\cos x\cos y\left(1 - \dfrac{\sin x}{\cos x}\cdot\dfrac{\sin y}{\cos y}\right)} \;=\;\frac{1}{\underbrace{\cos x\cos y - \sin x\sin y}_{\text{This is }\cos(x+y)}} . = \;\frac{1}{\cos(x+y)} \;=\;\sec(x+y)

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