Question

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

Answer 1

Any idea ?

Answer 2

half angle

Answer 3

\[\begin{align*}
\frac{\cos A}{1+\sin A}&=\frac{\sin(90+A)}{1-\cos(90+A)}\\
&=\frac{2\sin\left(45+\frac A2\right)\cos\left(90+\frac A2\right)}{2 \sin^2 \left(45+\frac A2\right)}\\&=\cot\left(45+\frac A2\right)
\end{align*}\]
So your identity is wrong.
For example substitute A=90, then,

LHS = 0/2 = 0
RHS = tan(45+45) =infinity => not equal.

Answer 4

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

Answer 5

seems that the identity is wrong.

Answer 6

Hmm the identity is definitely wrong.