I needd helppp. I can't verify this identity! Pleasee help and show full work. Thanks :)
I needd helppp. I can't verify this identity! Pleasee help and show full work. Thanks :)
Ok, you need to find some way to break down the 'cubes' in the cos and sin functions.
Separate the cos^3 and sin^3 into cos(x)cos^2(x) and sin(x)sin^2(x) respectively:
Use the identity cos^2(x) + sin^2(x) = 1:
Expand;
Rearrange;
Factor out cos(x)sin(x) from the two last terms in the numerator;
Factor out sin(x) + cos(x) from the numerator in all the terms together;
It's done now. :) Only one little step more.
If I may show another way.
Note the sum of two cubes in the numerator. Factoring it, gives:
The sin(x)+cos(x) cancels and we are left with:
Note the identity
This leaves us with
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