Solve T(t)=10(operatorname{ctg}pit/48-operatorname{ctg}pit/24)

$$T ( t ) = 10 ( \operatorname { ctg } \frac { \pi t } { 48 } - \operatorname { ctg } \frac { \pi t } { 24 } )$$

Solve for T

$$T=\frac{10}{t\sin(\frac{\pi t}{24})}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }t=24n_{1}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 10 by \cot(\frac{\pi t}{48})-\cot(\frac{\pi t}{24}).

$$Tt=10\cot(\frac{\pi t}{48})-10\cot(\frac{\pi t}{24})$$

The equation is in standard form.

$$tT=10\cot(\frac{\pi t}{48})-10\cot(\frac{\pi t}{24})$$

Divide both sides by t.

$$\frac{tT}{t}=\frac{10}{\sin(\frac{\pi t}{24})t}$$

Dividing by t undoes the multiplication by t.

$$T=\frac{10}{\sin(\frac{\pi t}{24})t}$$

Divide \frac{10}{\sin(\frac{\pi t}{24})} by t.

$$T=\frac{10}{t\sin(\frac{\pi t}{24})}$$