Question

Solve the following problems.

\( \frac{d y}{d t} \tan y=\sin (t+y)+\sin (t+y) \)

 

Answer 1

Solution 

Solve the following problems.

         \( \frac{d y}{d t} \tan y=\sin (t+y)+\sin (t+y) \)

\( \Longrightarrow \frac{d y}{d t} \tan y=2 \sin t \cos y \)

\( \Longrightarrow \frac{\tan y}{\cos y} d y=2 \sin t d t \)

\( \Longrightarrow \int \frac{\tan y}{\cos y} d y=2 \int \sin t d t \)

\( \Longrightarrow \sec y=-2 \cos t+C \)

Above integral explains below:

\( \int \frac{\tan y}{\cos y} d y =\int \tan y \cdot \frac{1}{\cos y} d y \)

                  \( =\int \tan y \sec y d y=\sec y+C \)

 

Therefore.   \( \sec y=-2 \cos t+C \)