упростите: sin (альфа - 3 пи/2)*cos(пи-альфа)- sin(альфа-пи)*sin(пи+альфа). Created by sahutagilev. algebra-ru

2)*cos(пи-альфа)- sin(альфа-пи)*sin(пи+альфа)...

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July 2022 1 3 Report

упростите: sin (альфа - 3 пи/2)*cos(пи-альфа)- sin(альфа-пи)*sin(пи+альфа)

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NNNLLL54

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$sin(a- \frac{3\pi }{2}) \cdot cos(\pi -a)-sin(a-\pi )\cdot sin(\pi +a)=\\\\= -sin(\frac{3\pi }{2}-a)\cdot (-cosa) +sin(\pi -a)\cdot (-sina)=\\\\=-sina\cdot cosa-sina\cdot sina=-sina(\underbrace {cosa+sina})=\\\\=-sina\cdot \underbrace {\sqrt2\; sin(\frac{\pi}{4}+a)}=-\sqrt2\cdot sina\cdot sin(\frac{\pi}{4}+a)$

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