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  1. MHB Apprentice

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    #1
    Can anybody please help me solve this?

    4cotē - 6 cosec x = -6

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    #2
    Quote Originally Posted by simongreen93 View Post
    Can anybody please help me solve this?

    4cotē - 6 cosec x = -6
    Good evening, what thoughts have you had to help solve this problem?


    I prefer to write everything in terms of sin and cos

    $ \displaystyle 4\dfrac{\cos^2(x)}{\sin^2(x)} - \dfrac{6}{\sin(x)} = -6$

    Some thoughts:

    • Clear the denominator by multiplying by the LCD of the terms above
    • Work only with one trig function - I would recommend sine as you have more of them - do you know of an identity to change your cos to sin?

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    #3
    Quote Originally Posted by simongreen93 View Post
    Can anybody please help me solve this?

    4cotē - 6 cosec x = -6
    Since $\displaystyle \begin{align*} 1 + \cot^2{(x)} \equiv \csc^2{(x)} \end{align*}$ that means

    $\displaystyle \begin{align*} 4\left[ \csc^2{(x)} - 1 \right] - 6\csc{(x)} &= -6 \\ 4\csc^2{(x)} - 4 - 6\csc{(x)} &= -6 \\ 4\csc^2{(x)} - 6\csc{(x)} + 2 &= 0 \\ 2\csc^2{(x)} - 3\csc{(x)} + 1 &= 0 \end{align*}$

    Now solve the resulting quadratic.

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