\begin{array}{l}{(\cos \operatorname{ec} \theta-\cot \theta)^{2}=\frac

1.	\begin{array}{l}{(\cos \operatorname{ec} \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta}} \\ {\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}=2 \sec A}\end{array}
Answer» LHS =cosA/(1+sinA) +(1+sinA)/cosA ={cos²A +(1+sinA)²}/cosA.(1+sinA) ={cos²A+1+sin²A+2sinA}/cosA.(1+sinA) use sin²∅ +cos²∅ =1 =(1+1+2sinA)/cosA(1+sinA) =2(1+sinA)/cosA(1+sinA) =2/cosA =2secA = RHS

\begin{array}{l}{(\cos \operatorname{ec} \theta-\cot \theta)^{2}=\frac{1-\cos \theta}{1+\cos \theta}} \\ {\frac{\cos A}{1+\sin A}+\frac{1+\sin A}{\cos A}=2 \sec A}\end{array}

Answer»

LHS =cosA/(1+sinA) +(1+sinA)/cosA

={cos²A +(1+sinA)²}/cosA.(1+sinA)

={cos²A+1+sin²A+2sinA}/cosA.(1+sinA)

use sin²∅ +cos²∅ =1

=(1+1+2sinA)/cosA(1+sinA)

=2(1+sinA)/cosA(1+sinA)

=2/cosA

=2secA = RHS