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# C3 Trigonometry using double angle formula

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1. 1) tan2A + 5tanA = 0
find all values for A between 0 and 2pi
I can find 0, pi and 2pi for answers but not the rest

2) Prove the identity tan2x - tanx = tanxsec2x
I can get as far as (2sinxcos^2x-sinxcos2x)/(cos2xcosx) but don't know where to go from there

3)Prove that (cosA + sin A)(cos2A + sin2A) = cosA + sin3A
After expanding brackets I'm not sure what to do next
2. (Original post by marmbite)
1) tan2A + 5tanA = 0
find all values for A between 0 and 2pi
I can find 0, pi and 2pi for answers but not the rest

2) Prove the identity tan2x - tanx = tanxsec2x
I can get as far as (2sinxcos^2x-sinxcos2x)/(cos2xcosx) but don't know where to go from there

3)Prove that (cosA + sin A)(cos2A + sin2A) = cosA + sin3A
After expanding brackets I'm not sure what to do next
For 1, use double angle formulae and see if you can factor out something to solve it. (Never cancel things out by division!)

For 3, think about how to apply addition formulae.
3. (Original post by SeanFM)
For 1, use double angle formulae and see if you can factor out something to solve it. (Never cancel things out by division!)
did that, got half the answers but for some reason my other half were wrong and I can;t work out why
I got to 10tan^A + 2tanA=0
which became 2tanA(tanA + 1) = 0
the answers I meant to be 0, 0.87, 2.27, pi, 4.01, 5.41, 2pi
I can't work out how to get the 0.87 and therefore can't get half the answers

(Original post by SeanFM)
For 3, think about how to apply addition formulae.
Tried this and got in a mess and couldn't see what to do with it, I'm not sure exactly where to apply the addition formulae, or should I just apply it to all the cos2As and sin2As?
4. (Original post by marmbite)
did that, got half the answers but for some reason my other half were wrong and I can;t work out why
I got to 10tan^A + 2tanA=0
which became 2tanA(tanA + 1) = 0
the answers I meant to be 0, 0.87, 2.27, pi, 4.01, 5.41, 2pi
I can't work out how to get the 0.87 and therefore can't get half the answers
How did you get from tan2a to 10tan^2(A)?

Tried this and got in a mess and couldn't see what to do with it, I'm not sure exactly where to apply the addition formulae, or should I just apply it to all the cos2As and sin2As?
It's slightly 'cheating' (well, not really..) but it's helpful to look at the right hand side. Think of, in sin(a+b) and cos(a+b) etc, what the a and b can be to leave you ending up with cosA + sin3A
5. (Original post by SeanFM)
How did you get from tan2a to 10tan^2(A)?
that's where I went wrong.
Found the problem now and got the right answer, I'd made a silly error when dealing with the fraction

(Original post by SeanFM)
It's slightly 'cheating' (well, not really..) but it's helpful to look at the right hand side. Think of, in sin(a+b) and cos(a+b) etc, what the a and b can be to leave you ending up with cosA + sin3A
I'll try this, thanks

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