SOLUTION: Can somebody help me by writing 4 cos 2θ sin 4θ as a sum or difference? Ty.

Algebra ->  Test -> SOLUTION: Can somebody help me by writing 4 cos 2θ sin 4θ as a sum or difference? Ty.      Log On


   



Question 1067701: Can somebody help me by writing 4 cos 2θ sin 4θ as a sum or difference? Ty.
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Can somebody help me by writing 4 cos 2θ sin 4θ as a sum or difference?
-----
a+b = 40
a-b = 20
----
2a = 60
a = 30
Then b = 10
------------------------
4[cos(20)*sin(40)] = 4[cos(20-40)+cos(20+40)]
= 4[cos(20)+cos(60)]
--------------
Cheers,
Stan H.
--------------

Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Can somebody help me by writing 4*cos(2*theta)*sin(4*theta) as a sum or difference? Ty.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There is a general formula of Trigonometry

.


See any serious textbook in Trigonometry or the lessons

    - FORMULAS FOR TRIGONOMETRIC FUNCTIONS

    - Product of trigonometric functions

in this site. 


This formula is FUNDAMENTAL, which means "everybody must know it".


According to this formula,

4%2Acos%282%2Atheta%29%2Asin%284%2Atheta%29 = 4%2A%281%2F2%29%2A%28sin%284%2Atheta-2%2Atheta%29+%2B+sin%284%2Atheta%2B2%2Atheta%29%29 = 2%2Asin%282%2Atheta%29+%2B+2%2Asin%286%2Atheta%29.

Answer. 4%2Acos%282%2Atheta%29%2Asin%284%2Atheta%29 = 2%2Asin%282%2Atheta%29+%2B+2%2Asin%286%2Atheta%29.