"Pre-Calc" Trig Review problems

raptoric

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May 10, 2016
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So I have my final next week (5/18) and just wanted to know how my professor got the answers to 2 of the problems (gave answers and understood all but these).

1. Simplify 5sin(x)cos(2x) => Should be (5/2)sin(4x)

2. Rewrite the left side to look like the right side:
1 - 2sin^2(x)cos^2(x) - 2sin^4(x) = cos(2x)

Any assistance would be appreciated. I tried many different permutations of trig identities but never got there. Even went online and used some we hadn't learned. Thanks.
 
So I have my final next week (5/18) and just wanted to know how my professor got the answers to 2 of the problems (gave answers and understood all but these).

1. Simplify 5sin(x)cos(2x) => Should be (5/2)sin(4x)

sin(2Θ) = 2*sin(Θ) * cos(Θ)

Continue.....


2. Rewrite the left side to look like the right side:
1 - 2sin^2(x)cos^2(x) - 2sin^4(x) = cos(2x)

= 1 - 2sin^2(x)[cos^2(x) - sin^2(x)]

continue...

Any assistance would be appreciated. I tried many different permutations of trig identities but never got there. Even went online and used some we hadn't learned. Thanks.
.
 
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