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    I need some help with these exam questions. Struggling with the proof of trig identities.

    Thanks.


    https://www.dropbox.com/sh/q829c1wi8...MwqF8Ra1a?dl=0
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    (Original post by Jeevs090909)
    I need some help with these exam questions. Struggling with the proof of trig identities.

    Thanks.
    https://www.dropbox.com/sh/q829c1wi8...MwqF8Ra1a?dl=0
    \displaystyle \mathrm{cosec \ } x \equiv \sec x + \frac{2 \cot 2x}{\sin x + \cos x}

    Start with the RHS. Express everything in terms of sin and cos, then get it under the same denominator.
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    (Original post by RDKGames)
    \displaystyle \mathrm{cosec \ } x \equiv \sec x + \frac{2 \cot 2x}{\sin x + \cos x}

    Start with the RHS. Express everything in terms of sin and cos, then get it under the same denominator.
    Thanks
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    (Original post by Jeevs090909)
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    For the circle question, you simply need to get it in the form (x-a)^2+(y-b)^2 = r^2 before you answer the questions. After you do that, part (a) is just to read off the centre. Then for part (b), you need to know that r^2 > 0 and hence whatever you end up with on the RHS in terms of k, make that > 0 and hence deduce the inequality for k
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    (Original post by Jeevs090909)
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    For the other identity question, again, just express the LHS in terms of sines and cosines, get it under the same denominator, then spot the identity \sin 2\theta = 2 \cos \theta \sin \theta and use it before coming to a stop at the required result.
    For part b, just set the RHS of the identity equal to 1 and observe further what happens why the equality yields no solutions.
 
 
 
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