How to show that the left hand side of the below equation equals the right hand side ?
$\dfrac{cos A}{1+sin A} = tan(45+\dfrac{A}{2}) $

Question

anonymous · Answer

Any idea ?

experimentx · Answer

half angle

badhi · Answer

$$\begin{align*}
\frac{\cos A}{1+\sin A}&=\frac{\sin(90+A)}{1-\cos(90+A)}\
&=\frac{2\sin\left(45+\frac A2\right)\cos\left(90+\frac A2\right)}{2 \sin^2 \left(45+\frac A2\right)}\&=\cot\left(45+\frac A2\right)
\end{align*}$$
So your identity is wrong. 
For example substitute A=90, then,

LHS = 0/2 = 0
RHS = tan(45+45) =infinity => not equal.

anonymous · Answer

Should I take half angles for cos A and sin A too ?

experimentx · Answer

seems that the identity is wrong.

anonymous · Answer

Hmm the identity is definitely wrong.