Question

For all angles A + 2ine!
sin 2 Acos A
(1 + cos2.A)(1 + cos A)​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ \frac{ \sin 2A}{1 + \cos 2A} \times \frac{ \cos A}{1 + \cos A} }$

EVALUATION

$\displaystyle \sf{ \frac{ \sin 2A}{1 + \cos 2A} \times \frac{ \cos A}{1 + \cos A} }$

$\displaystyle \sf{ = \frac{2 \sin A \: \cos A}{2 { \cos}^{2}A } \times \frac{ \cos A}{1 + \cos A} }$

$\displaystyle \sf{ = \frac{\sin A \:}{ { \cos}^{}A } \times \frac{ \cos A}{1 + \cos A} }$

$\displaystyle \sf{ = \frac{ \sin A}{1 + \cos A} }$

$\displaystyle \sf{ = \frac{2 \sin \frac{A}{2} \: \cos \frac{A}{2} }{2 { \cos}^{2} \frac{A}{2} } }$

$\displaystyle \sf{ = \frac{\sin \frac{A}{2} \: }{ { \cos}^{} \frac{A}{2} } }$

$\displaystyle \sf{ =\tan \frac{A}{2}}$

FINAL ANSWER

$\boxed{ \: \: \displaystyle \sf{ \frac{ \sin 2A}{1 + \cos 2A} \times \frac{ \cos A}{1 + \cos A} }=\tan \frac{A}{2} \: \: }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. In a triangle, prove that (b+c-a)(cotB/2+cotC/2)=2a×cotA/2

https://brainly.in/question/19793971

2. prove that :

tan9A - tan6A -tan3A = tan9A.tan 6A.tan tan 3A

https://brainly.in/question/9394506