Question

prove : sin A/(1+cos A) = tan 1/2 A

Answer 1

multiply top and bottom by (1-cos A)

Answer 2

[sin A ( 1 - cos A)] / [( 1 + cos A) ( 1 - cos A) ]

Answer 3

the numerator is sin A - sin A cos A , the denominator is
1 - cos ^2 A , , which is equal to sin^2 A

Answer 4

hmm, its easier if you start from the right side

Answer 5

haha so are we gonna start from the right side?i have absolutely no idea how to solve.

Answer 6

Let b = 1/2 A
\[\sin2b/(1+\cos2b) = 2\sin(b)\cos(b)/(1+\cos^2(b)-\sin^2(b))\]
\[1 = \sin^2() + \cos^2()\]
\[\sin2b/(1+\cos2b) = 2\sin(b)\cos(b)/(\cos^2(b)+sin^2(b)+\cos^2(b)-\sin^2(b))\]
\[=2\sin(b)\cos(b)/2\cos^2(b) = \sin(b)/\cos(b) = \tan(b) = \tan(1/2A)\]

Answer 7

there is a tan half formula ?

Answer 8

tan (1/2 A) =
sin (1/2 A ) / cos (1/2 A)

Answer 9

\[sinA=2\sin(\frac{A}{2})\cos(\frac{A}{2})\]\[cosA=2\cos^2(\frac{A}{2})-1\]
therfore
\[\frac{2\sin(\frac{A}{2})\cos(\frac{A}{2})}{2\cos^2(\frac{A}{2})} \]\[=\frac{\sin(\frac{A}{2})}{\cos(\frac{A}{2})} = \tan(\frac{A}{2})\]

Answer 10

THANKS lalaly and others for the answers.much appreciated people.

Answer 11

ur welcome:)

Answer 12

wait theres a mistak

Answer 13

sin (a/2) = ?

Answer 14

oh i see , you multiplied top and bottom by 2 cos (a/2)

Answer 15

me?

Answer 16

i didnt multiply anything, i used the trigonometric identities

Answer 17

im coming from the right side of the equation

Answer 18

that gives me the clue to use half angle formula

Answer 19

but youre way works