Verify the identity cotx minus pi divided by two x

Asked by maham237 @ 14/07/2021 in Mathematics viewed by 630 People

Answered by maham237 @ 14/07/2021

$\bf \textit{Sum and Difference Identities}
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sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)
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cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\
-------------------------------\\\\

cot\left(x-\frac{\pi }{2} \right)=-tan(x)\\\\
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$\bf cot\left(x-\frac{\pi }{2} \right)\implies \cfrac{cos\left(x-\frac{\pi }{2} \right)}{sin\left(x-\frac{\pi }{2} \right)}\implies \cfrac{cos(x)cos\left( \frac{\pi }{2} \right)+sin(x)sin\left( \frac{\pi }{2} \right)}{sin(x)cos\left( \frac{\pi }{2} \right)-cos(x)sin\left( \frac{\pi }{2} \right)}
\\\\\\
\cfrac{cos(x)\boxed{0}+sin(x)\boxed{1}}{sin(x)\boxed{0}-cos(x)\boxed{1}}\implies \cfrac{sin(x)}{-cos(x)}\implies -tan(x)$

Verify the identity cotx minus pi divided by two x

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