Question

solve the equation on the interval 0 ≤ θ < 2π (cotθ-1)(cscθ+1)=0

Answer 1

\[either~\cot \theta-1=0,\cot \theta =1 ,\frac{ 1 }{\tan \theta }=1,\tan \theta=1\]
\[\tan \theta=1=\tan \frac{ \pi }{4 },\tan \left( \pi+\frac{ \pi }{4 } \right),\theta=\frac{\pi }{ 4 },\frac{ 5 \pi }{ 4 }\]
similarly \[\csc \theta=-1,\]
change in sin and find the value of theta.