Mathematics, 24.10.2019 17:43 salinasroel22
Find the expansion for cos 6 theta and sin 6 theta
Answers: 3
and 
is given below and this can be evaluated by using the trigonometric properties. 
![\bf cos(6\theta)\implies cos(3\theta+3\theta)\implies cos[2(3\theta)] \\\\\\ now\implies \begin{cases} cos(3x)=4cos^3(x)-3cos(x)\\\\ cos(2x)=2cos^2(x)-1 \end{cases} \\\\\\ cos[2(3\theta)]\implies 2\left[ 4cos^3(\theta)-3cos(\theta) \right]^2-1](/tpl/images/0344/6767/cee7b.png)
![\bf sin(6\theta)\implies sin(3\theta+3\theta)\implies sin[2(3\theta)] \\\\\\ now\implies \begin{cases} sin(2x)=2cos(x)sin(x)\\\\ sin(3x)=3sin(x)-4sin^3(x) \end{cases} \\\\\\ sin[2(3\theta)]\implies 2cos(3\theta)sin(3\theta) \\\\\\ 2\ [4cos^3(\theta)-3cos(\theta)]\ [3sin(\theta)-4sin^3(\theta)]](/tpl/images/0344/6767/6e4b9.png)
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Find the expansion for cos 6 theta and sin 6 theta...
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