SOLUTION: Hi, can someone help me in the 2nd part to find x. Question: By writing cos 4x = cos (3x+x) and cos 2x = cos (3x-x), show that cos 2x + cos 4x = 2cos3xcosx and cos 2x – cos 4x

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, can someone help me in the 2nd part to find x. Question: By writing cos 4x = cos (3x+x) and cos 2x = cos (3x-x), show that cos 2x + cos 4x = 2cos3xcosx and cos 2x – cos 4x       Log On


   

Question 1056981: Hi, can someone help me in the 2nd part to find x.
Question:
By writing cos 4x = cos (3x+x) and cos 2x = cos (3x-x), show that cos 2x + cos 4x = 2cos3xcosx and cos 2x – cos 4x = 2sin3xsinx.
Given further that cos3xcosx = 0.683 and sin3xsinx = 0.183, find the value of x where 0° < x < 180°.
Thank you very much.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
highlight_green%28cos%28x%2By%29=cos%28x%29cos%28y%29-sin%28x%29sin%28y%29%29
highlight_green%28cos%28x-y%29=cos%28x%29cos%28y%29%2Bsin%28x%29sin%28y%29%29
-----------------------------------------------------


cos%282x%29%2Bcos%284x%29=2cos%283x%29cos%28x%29
cos%283x-x%29%2Bcos%283x%2Bx%29
cos%283x%29cos%28x%29%2Bsin%283x%29sin%28x%29%2Bcos%283x%29cos%28x%29-sin%283x%29sin%28x%29
Using commutative property of equality,
cos%283x%29cos%28x%29%2Bcos%283x%29cos%28x%29%2Bsin%283x%29sin%28x%29-sin%283x%29sin%28x%29
2cos%283x%29cos%28x%29=RightHandSide


Very straightforward if you know or have reference to the two identities.


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The second part if you will look carefully, only depends on simple substitution. Note also that the sine information in not needed.