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Trig Identity proof

  1. Apr 6, 2013 #1

    trollcast

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    Gold Member

    1. The problem statement, all variables and given/known data

    Prove the identity:

    $$\csc(2\theta)-\cot(2\theta)\equiv\tan(\theta)$$


    2. Relevant equations

    3. The attempt at a solution

    Starting with the LHS:

    $$\csc(2\theta)-\cot(2\theta)$$
    $$\frac{1}{\sin(2\theta)}-\frac{\cos(2\theta)}{\sin(2\theta)}$$
    $$\frac{1-\cos(2\theta)}{sin(2\theta)}$$

    And thats as far as I can see to rearrange it.
     
  2. jcsd
  3. Apr 6, 2013 #2

    rock.freak667

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    Homework Helper

    Now just substitute your identities for cos2θ and sin2θ and it should work out easily.
     
  4. Apr 6, 2013 #3

    trollcast

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    Gold Member

    Woops I forgot about the double angle formulae

    so the rest of it is:

    $$\frac{1-(1-2\sin^2(\theta))}{2sin(\theta)\cos(\theta)}$$
    $$\frac{2\sin^2(\theta)}{2sin(\theta)\cos(\theta)}$$
    $$\frac{sin(\theta)}{\cos(\theta)}$$
    $$=\tan(\theta)$$
    ∴ LHS = RHS
     
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