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# C3 compound angles??? helppppp watch

1. i'm struggling with proof questions for compound angle formula! I start the questions and get stuck halfway through them.

11. tanA + cotA ≡ 2cosecA
LHS:
tanA + 1/tanA

= sinA/cosA + cosA/sinA

= sinA(sinA)/cosAsinA + cosA(cosA)/cosAsinA
.... and then i'm not sure how to carry on!

same with this question:
cotA - tanA ≡ 2cot2A
LHS:

1/tanA - tanA

= cosA/sinA - sinA/cosA

= cosA(cosA)/sinAcosA - sinA(sinA)/sinAcosA

= cos^2A/sinAcosA - sin^2A/sinAcosA

= (1 - sin^2A)/sinAcosA - (1-cos^2A)/sinAcosA
..... aaand i'm stuck again.

let alone these two questions that I don't even know where to start from, where I have to solve for θ between 0 and 2pi inclusive.

1. sin(x + 60) + cos( x+30) =1/2

4. 4cos2θ - 6cosθ + 5 = 0

Help?? im desperate
2. Well for the first one I think you have written it wrong it should be tanA + cotA ≡ 2cosec(2A).

Your working up to now is fine add the two fractions you have together (they have the same denominator so that's easy), now look at the numerator this is a very well know identity so you can simplify it a whole lot. Then you need to deal with the sinxcosx on the bottom now we know sin(2x)=sin(x + x) = sin(x)cos(x) + cos(x)sin(x) = 2sin(x)cos(x) so account for the factor of 2 and then it should be obvious.

The other ones are on the same lines just see how you can get to what you want using the identities you know. Double angle etc.

(Original post by hellojadey)
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3. isn't it sin^2 + cos^A/ cosAsinA ?
how can i use the formula of none is of 2A?

Posted from TSR Mobile
4. (Original post by hellojadey)
isn't it sin^2 + cos^A/ cosAsinA ?
how can i use the formula of none is of 2A?

Posted from TSR Mobile
Yes that is correct. But what identity do you know involving sin^2(A)+cos^2(A)?

Then you just need to figure out what cosAsinA is equal to (re-read my old post to see).

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