If tan A 2 = 3 2 , then 1 + c o s A 1 − c o s A = Options: A . &nbsp -5 B . &nbsp 5 C . &nbsp 9 4 D . &nbsp 4 9

Answer: Option D : D Given that tan A 2 = 3 2 . 1 + c o s A 1 − c o s A = 2 c o s 2 A 2 2 s i n 2 A 2 = c o t 2 A 2 = ( 2 3 ) 2 = 4 9

If tan A2 = 32, then 1+cosA1−cosA =

Discussion Forum : Trigonometric Functions

Question -

If tan
$\frac{A}{2}$ =
$\frac{3}{2}$ , then
$\frac{1 + c o s A}{1 - c o s A}$ =

Options:

A . -5

B . 5

C .

\frac{9}{4}

D .

\frac{4}{9}

Answer: Option D
:
D

Given that tan
$\frac{A}{2}$ =
$\frac{3}{2}$ .

$\frac{1 + c o s A}{1 - c o s A}$ =
$\frac{2 c o s^{2} \frac{A}{2}}{2 s i n^{2} \frac{A}{2}}$ = $c o t^{2} \frac{A}{2}$ = ${(\frac{2}{3})}^{2}$ =
$\frac{4}{9}$

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