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Math Help - Trig Identities and Equations

  1. #1
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    Trig Identities and Equations

    Verifiy the following identites letting @=theta.

    1. cos@= sec@ - sin@tan@

    2. sin@ cos@
    ----- + ----- = 1
    csc@ sec@

    3. 1+cos@= cot@(sin@+tan@)

    4. (1+cot@)^2=csc^2@+2cot@
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  2. #2
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    Quote Originally Posted by daviskane View Post
    3. 1+cos@= cot@(sin@+tan@)
    You already asked the first two in a different post! Please don't double post.

    3. 1 + cos(\theta) = cot(\theta)(sin(\theta) + tan(\theta))

    The RHS:
    cot(\theta)(sin(\theta) + tan(\theta))

    = cot(\theta) \cdot sin(\theta) + 1

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

    = cos(\theta) + 1
    which is the LHS.

    -Dan
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  3. #3
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    Hello, daviskane!

    Verifiy: . 4)\;(1+\cot\theta)^2\:=\:\csc^2\!\theta+2\cot\thet  a

    The left side is: . (1 + \cot\theta)^2 \:=\:1 + 2\cot\theta + \cot^2\!\theta

    . . = \;\underbrace{(1 + \cot^2\!\theta)}_{\text{this is }\csc^2\!\theta} + \,2\cot\theta \;=\;\csc^2\!\theta + 2\cot\theta

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