- #1
UrbanXrisis
- 1,196
- 1
1. Express [tex] \frac{sin^2 2 \theta}{1+cos^2 2 \theta} [/tex] as a function of [tex]sin \theta[/tex]
here's what I did:
[tex] = \frac{4 sin^2 \theta cos^2 \theta}{1+(2cos^2 \theta -1)^2} [/tex]
[tex] = \frac{4 sin^2 \theta cos^2 \theta}{1+(4cos^4 \theta - 4 cos^2 \theta + 1)} [/tex]
[tex] = \frac{2sin^2 \theta cos^2 \theta}{2cos^2 \theta - 2cos^2 \theta +1} [/tex]
is this correct? can I simplify it more?
2. Write [tex]sin(a+b)sin(a-b)[/tex] as a function of double angles
I used the sum and product formulas to simplify the equation but I did not use the double angle formulas. I'm not quite sure what the question is asking.
Here's what I did:
[tex] = .5 [cos(a+b-a+b)-cos(a+b+a-b)] [/tex]
[tex] = .5 [cos(2b)-cos(2a)] [/tex]
not sure where the double anges come in. any ideas?
3. simplify [tex] \sqrt{2-2cos4 \Theta}[/tex]
i can make it become 1-cos4x but I don't know how to simplify it further because of the cos4. no clue on this one, any help would be appreciated.
here's what I did:
[tex] = \frac{4 sin^2 \theta cos^2 \theta}{1+(2cos^2 \theta -1)^2} [/tex]
[tex] = \frac{4 sin^2 \theta cos^2 \theta}{1+(4cos^4 \theta - 4 cos^2 \theta + 1)} [/tex]
[tex] = \frac{2sin^2 \theta cos^2 \theta}{2cos^2 \theta - 2cos^2 \theta +1} [/tex]
is this correct? can I simplify it more?
2. Write [tex]sin(a+b)sin(a-b)[/tex] as a function of double angles
I used the sum and product formulas to simplify the equation but I did not use the double angle formulas. I'm not quite sure what the question is asking.
Here's what I did:
[tex] = .5 [cos(a+b-a+b)-cos(a+b+a-b)] [/tex]
[tex] = .5 [cos(2b)-cos(2a)] [/tex]
not sure where the double anges come in. any ideas?
3. simplify [tex] \sqrt{2-2cos4 \Theta}[/tex]
i can make it become 1-cos4x but I don't know how to simplify it further because of the cos4. no clue on this one, any help would be appreciated.
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