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Question Number 193669 by Rupesh123 last updated on 17/Jun/23

Answered by deleteduser1 last updated on 18/Jun/23

$$cos(x+y)+isin(x+y)=e^{i(x+y)}=e^{ix}{e}^{iy}$$$$=(cos\left(x\right)+isin\left(x\right))(cos\left(y\right)+isin\left(y\right))$$$$=cos\left(x\right)cos\left(y\right)-sin\left(x\right)cos\left(y\right)+icos\left(x\right)sin\left(y\right)+isin\left(x\right)cos\left(y\right)$$$$Comparingrealparts$$$$\Rightarrow cos(x+y)=cos\left(x\right)cos\left(y\right)-sin\left(x\right)cos\left(y\right)$$

Commented by Rupesh123 last updated on 18/Jun/23

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