Expand Using Sum/Difference Formulas cot((25pi)/2+t)

$\cot (\frac{25 π}{2} + t)$

Replace $\cot (\frac{25 π}{2} + t)$ with an equivalent expression $\frac{1}{\tan (\frac{25 π}{2} + t)}$ using the fundamental identities.

$\frac{1}{\tan (\frac{25 π}{2} + t)}$

Simplify.

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Rewrite $\tan (\frac{25 π}{2} + t)$ in terms of sines and cosines.

$\frac{1}{\frac{\sin (\frac{25 π}{2} + t)}{\cos (\frac{25 π}{2} + t)}}$

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (\frac{25 π}{2} + t)}{\cos (\frac{25 π}{2} + t)}$ .

$\frac{\cos (\frac{25 π}{2} + t)}{\sin (\frac{25 π}{2} + t)}$

Convert from $\frac{\cos (\frac{25 π}{2} + t)}{\sin (\frac{25 π}{2} + t)}$ to $\cot (\frac{25 π}{2} + t)$ .

$\cot (\frac{25 π}{2} + t)$

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