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Question 3.4

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TZ
leumasicOfficial

3 months ago

i)

S(P(y))=S(2y)=(2y)2=22y.S(P(y))=S(2^y)=(2^y)^2=2^{2y}.

ii)

S(s(y))=S(sin⁡y)=sin⁡2y.S(s(y))=S(\sin y)=\sin^2 y.

iii)

S(P(s(t)))+s(P(t))=S(P(sin⁡t))+s(2t)=S(2sin⁡t)+sin⁡(2t)=22sin⁡t+sin⁡2t.\begin{align*} S(P(s(t)))+s(P(t)) &= S(P(\sin t))+s(2^t) \\ &= S(2^{\sin t})+\sin(2^t) \\ &= 2^{2\sin t}+\sin 2^t. \end{align*}

iv)

S(t3)=sin⁡t3.S(t^3)=\sin t^3.
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