i'm struggling with proof questions for compound angle formula! I start the questions and get stuck halfway through them.
11. tanA + cotA ≡ 2cosecA
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
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
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C3 compound angles??? helppppp watch
- Thread Starter
- 11-09-2015 13:18
- 11-09-2015 13:30
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.
- Thread Starter
- 11-09-2015 14:07
isn't it sin^2 + cos^A/ cosAsinA ?
how can i use the formula of none is of 2A?
Posted from TSR Mobile
- 11-09-2015 16:00
Then you just need to figure out what cosAsinA is equal to (re-read my old post to see).