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Math Help - Trig. problems.

  1. #1
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    Question Trig. problems.

    Hi,

    Can someone help me to do these problems?

    1).If tan(θ+α)-(3+2√2)tanθ = 0,
    Prove that, sin(2θ+α )= √2sinα

    2).Prove that, cos⁻x-sin⁻x= π/6
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  2. #2
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    Hello, Malsha!

    2) Prove that: cos⁻x-sin⁻x= π/6
    Could that be: . \cos^{\text{-}1}x - \sin^{\text{-}1}x \:=\:\frac{\pi}{6}\;?\quad\hdots This is not true!


    \text{We have: }\;\underbrace{\cos^{\text{-}1}x}_{\alpha} - \underbrace{\sin^{\text{-}1}x}_{\beta}

    That is: . \begin{array}{ccc}\alpha \:=\:\cos^{-1}x & \Rightarrow & \cos\alpha \:=\:x \\<br />
\beta \:=\:\sin^{-1}x & \Rightarrow & \sin\beta \:=\:x \end{array}


    We have: . \begin{array}{ccccc}\cos\alpha &=&\dfrac{x}{1} &=& \dfrac{adj}{hyp} \\ \\[-3mm] \sin\beta &=& \dfrac{x}{1} &=& \dfrac{opp}{hyp} \end{array}


    Hence, the two angles are in this triangle.
    Code:
                            *
                         * β*
                  1   *     *
                   *        *
                *           *
             * α            *
          *  *  *  *  *  *  *
                   x

    And we see that the two angles are complementary: . \alpha + \beta \:=\:\frac{\pi}{2}

    So their sum is a constant, but not their difference.

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