Verify this is an Identity:
cos t + cos3t/sin t - sin 3t = -cot t

This is what I have so far,
cos t + cos3t/sin t - sin 3t = -cot t

cos t + (4cos^3 t - 2 cos t)/sin t -(3sin t - 4sin^3 t) = -cot t

cos t + cos t(1+3cos^3t - 2 cos t)/sin t - sin(1-2sin t - 3sin^3 t) = -cot t

2cos t (1+3cos^3t - 2 cos t)/ -2sin t(1-2sin t - 3sin^3 t) = -cot t

Question

Verify this is an Identity:
cos t + cos3t/sin t - sin 3t = -cot t 

This is what I have so far,
cos t + cos3t/sin t - sin 3t = -cot t 

cos t + (4cos^3 t - 2 cos t)/sin t -(3sin t - 4sin^3 t) = -cot t

cos t + cos t(1+3cos^3t - 2 cos t)/sin t - sin(1-2sin t - 3sin^3 t) = -cot t

2cos t (1+3cos^3t - 2 cos t)/ -2sin t(1-2sin t - 3sin^3 t) = -cot t

anonymous · Answer

I'm confused on what to do next.

chihiroasleaf · Answer

I think you did some mistakes,
$$\cos (3t) = 4 \cos ^{3} (t) - 3 \cos (t)$$

hartnn · Answer

alternative way : 
use
 SinC - SinD = 2Cos[(C+D)/2]Sin[(C-D)/2]

CosC + CosD = 2Cos[(C+D)/2]Cos[(C-D)/2]

hartnn · Answer

C=t, D=3t

chihiroasleaf · Answer

well, I got confused about the problems, 
which one is the left side? 
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