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# C3 Trig watch

1. So I'm doing this question:

Prove that
sec x -1 / sec x +1 = tan^2(x/2)

I've managed to get to 1 - cos x / 1 + cos x but the textbook says the next step is
1 - (1 - 2 sin^2 (x/2)) / 1 + (2 cos^2(x/2) - 1 )
But I have literally no idea how that's happened... can anyone help? D;
2. Double angle formulae is what I'm guessing should be the next step
3. (Original post by white_o)
So I'm doing this question:

Prove that
sec x -1 / sec x +1 = tan^2(x/2)

I've managed to get to 1 - cos x / 1 + cos x but the textbook says the next step is
1 - (1 - 2 sin^2 (x/2)) / 1 + (2 cos^2(x/2) - 1 )
But I have literally no idea how that's happened... can anyone help? D;

cosθ = 2cos2(1/2θ) - 1
cos2θ = 2cos2θ - 1
cos3θ = 2cos2(3/2θ) - 1
cos4θ = 2cos2(2θ) - 1
cos5θ = 2cos2(5/2θ) - 1
4. Hope this helps!

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Updated: October 21, 2015
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