Simplify the trigonometric expression cot(2pi+(7*-pi)/4)

 Exercise

$\cot\left(2\pi-\frac{7\pi}{4}\right)$

 

Combine all terms into a single fraction with $4$ as common denominator

$\cot\left(\frac{8\pi +7\cdot -\pi }{4}\right)$

 

Combining like terms $8\pi $ and $7\cdot -\pi $

$\cot\left(\frac{\left(8-7\right)\pi }{4}\right)$

 

Subtract the values $8$ and $-7$

$\cot\left(\frac{1\pi }{4}\right)$

 

Any expression multiplied by $1$ is equal to itself

$\cot\left(\frac{\pi }{4}\right)$

 

Calculating the cotangent of $\frac{\pi }{4}$ degrees

$1$

$1$

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