looks like the exponents did not show up, in the first it should be 4 cosine cubed x - 3cosx
and the sin 3x should be 3sinx - 4sine cubed x
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The period of sin + cos is 2*pi radians (360 degrees) so the period of sin(3x) + cos(3x) is 2*pi/3 radians.
0. sin 2x = cos 3x 1. sin 2x = sin (pi/2 - 3x) [because cos u = sin (pi/2 - u)] 2. [...]
cos(x)-cos(x)sin2(x)=[cos(x)][1-sin2(x)]cos(x)-cos(x)sin2(x)=[cos(x)][cos2(x)]cos(x)-cos(x)sin2(x)=cos3(x)
a formula is a formula <3 simples!
This is a perfect time to use l'Hospital's rule: If a fraction becomes 0/0 at the limit (like this one does), then the limit of the fraction is equal to the limit of (derivative of the numerator)/(derivative of the denominator) . I'm not sure why l'Hospital's rule stuck with me all these years. But when it's appropriate, like for this one, you can't beat it.