Question

tana/2= 3/2 then 1+cosa/1-cosa =

Answer 1

Answer :

We know that,

cosA

= 2 cos²(A/2) - 1

= 1 - 2 sin²(A/2)

Now, (1 + cosA)/(1 - cosA)

= {1 + 2 cos²(A/2)- 1}/{1 - 1 + 2 sin²(A/2)}

= cos²(A/2) / sin²(A/2)

= 1/tan²(A/2)

= 1/(3/2)²

= 1/(9/4)

= 4/9

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Answer 2

Answer: Value of  (1+cosa)/(1-cosa) is  4/9

Step-by-step explanation:

Substitute cos(a) in terms of cos(a/2) and sin(a/2)

$cos(a) = cos^{2} (\frac{a}{2} ) - sin^{2} (\frac{a}{2} )\\\frac{1+cos(a)}{1- cos(a)} \\\frac{(1 + cos^{2} (\frac{a}{2} ) - sin^{2} (\frac{a}{2} ) )}{(1 -cos^{2} (\frac{a}{2} ) +sin^{2} (\frac{a}{2} ) )} \\\frac{2 cos^{2} (\frac{a}{2} )}{2sin^{2} (\frac{a}{2} ) } \\ cot^{2} (\frac{a}{2} )$

As tan(a/2) = 3/2,

$cot(\frac{a}{2}) = \frac{2}{3}$

$cot^{2} (\frac{a}{2}) = (\frac{2}{3})^{2}$

$cot^{2} (\frac{a}{2}) = \frac{4}{9}$

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