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# Quick indentities Q (P2) watch

1. I'm looking at the mark scheme for the question 1-Tan A/1+Tan A = Cos 2A

It's fine until they get from 1-(Sin^2 A/Cos^2 A)/1+(Sin^2 A/Cos^2 A) to (Sin^2 A - Cos^2 A) / (Sin^2 A + Cos^2 A)

Can someone explain how to go from the 1st part to the second part? Thanks.
2. (Original post by MJ_23)
It's fine until they get from 1-(Sin^2 A/Cos^2 A)/1+(Sin^2 A/Cos^2 A) to (Sin^2 A - Cos^2 A) / (Sin^2 A + Cos^2 A)
I think you've made a couple of typos - missing the ^2 from the tans and also getting the numerator the wrong way round at the end. Anyway:

If you put both the numerator and denominator as single fractions with cos^2 A on the bottom, you have[(cos^2 A - sin^2 A)/cos^2 A] / [(cos^2 A + sin^2 A)/cos^2 A] the cos^2 A cancel so you're left with (cos^2 A - sin^2 A) / (sin^2 A + cos^2 A)
sin^2 A + cos^2 A = 1 and cos^2 A - sin^2 A = cos2A so this equals cos(2A)

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