How do I rewrite \(\displaystyle{\left({\left({\cos{{t}}}\right)}^{{3}}\right)}-{2}{\left({\left({\cos{{t}}}\right)}\cdot{\left({\left({\sin{{t}}}\right)}^{{2}}\right)}\right)}\) to

Aliyah Mendez

Aliyah Mendez

Answered question

2022-04-16

How do I rewrite ((cost)3)2((cost)((sint)2)) to 3(cost)32cost ?

Answer & Explanation

fallendreamsit2p

fallendreamsit2p

Beginner2022-04-17Added 14 answers

First, we denote (cost)3 as cos3t and (sint)2=sin2t
Then we use the identity
sin2t+cos2t=1sin2t=1cos2t
and simplify.
cos3t2costsin2t=cos3t2cost(1cos2t)
=cos3t2cost+2cos3t
=3cos3t2cost

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