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# Trig Identities help! watch

1. Is it possible to write ( 1-sin²θ/sinθ ) as 1/sinθ-sinθ

Also I am really confused on what to do to prove the following:
1] ( sin2θ+sinθ ) / ( 1+cos2θ+cosθ ) ≡tanθ
2] ( 1-cos2θ+sin2θ ) / ( 1+cos2θ+sin2θ ) ≡tanθ

I've started with LHS = and then i get stuck

2. You need to get some brackets in there or use latex, what you have written is ambiguous without.
3. You should put parenthesis, it is quite confusing...
If it is (1-sin²)/(sin), then it is equal to (1/sin)-sin because sin²/sin just gives you sin
If it is 1-(sin²/sin), then it gives 1-sin

1) and 2) => put parenthesis, and someone might help
4. 1) It is very easy, just replace the ones with "2x" using the duplication formulae

[sin(2x)+sin(x)]/(1+cos(2x)+cos(x)) = (2sin(x)cos(x)+sin(x))/(1+(cos²x-sin²x)+cos(x)
= [(sin(x)(2cos(x)+1)]/[(cos(x)(2cos(x)+1)]
= sin(x)/cos(x)
= tan(x)

2) [(1-cos(2x)+sin(2x)]/[(1-cos(2x)+sin(2x)] = 1...you should have made a mistake here
5. 2nd one should have a + after the 1 not a minus
my mistake

should be ( 1-cos2θ+sin2θ ) / ( 1+cos2θ+sin2θ ) ≡tanθ
6. then you have
2) LHS = 1 - (cos²x - sin²x) + 2sin(x)cos(x)
=2sin²x+2sin(x)cos(x)
= 2sin(x)(sin(x)+cos(x)

RHS=1+cos²x-sin²x +2sin(x)cos(x)
= 2cos²(x)+2sin(x)cos(x)
=2cos(x)(cos(x)+sin(x)

LHS/RHS = sin(x)/cos(x) = tan(x)
7. Thanks

do you know how to get the maximum and minimum of acos(x)+bsin(x)?
8. Well, if you do not want to use calculus, you have
-1<cos(x)<1 (it can also be EQUAL, but I do not know how to write it without latex)
Therefore, for a>0, -a<acos(x)<a
For a<0, then it would change the sign, but basically since you have a on the LHS and RHS, it would not change much

Then , you do the same for b, you take into account the signs of a and of b, and here you are
9. for example i've done cosx- root3 sinx=2
in the for Rcos(x-a) gives 2cos(x- [root3/1]

how would i get the max/min for this?
10. I do not really understand...for f(x)=acos(x)+bsin(x), do you want to solve f(x) = k, where k is a constant, or just find the variations of the function f?
11. i dont know! my teacher taught us this but i didnt get any of it!
12. (Original post by notan123)
for example i've done cosx- root3 sinx=2
in the for Rcos(x-a) gives 2cos(x- [root3/1]

how would i get the max/min for this?
Can you state the maximum and minimum of f(x) = cos x ?

What about y = f (x - k) ?

What about y = 2 f (x - k) ?

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Updated: January 30, 2010
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