SOLUTION: Question 624957: Verify the trig identity: sin^4(x)+cos^4 (x)=3/4 + 1/4 cos(4x).
How about this solution (different and faster than from jsmallt9):
sin^4(x)+cos^4(x) = ((sin^2
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Question 624980: Question 624957: Verify the trig identity: sin^4(x)+cos^4 (x)=3/4 + 1/4 cos(4x).
How about this solution (different and faster than from jsmallt9):
sin^4(x)+cos^4(x) = ((sin^2(x) + cos^2(x)))^2 - 2sin^2(x)cos^2(x) =
1 - 2sin^2(x)cos^2(x) = 1 - (1/2)sin^2(2x) = 1 - (1 - cos(4x))/4 =
1 - 1/4 + cos(4x)/4 = 3/4 + cos(4x)/4 Done
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
This solution works, too.
The main reason it appears faster than my solutions is that many intermediate steps are being omitted. If I had done this my first solution would look like:
And we're finished!
And the second solution would be:
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