Question

630°<A<720° and tanA=12/5 then tanA/2​

Answer 1

Hello Friend..♥️♥️

Ans

Is in the pic

Thank you

Answer 2

Given,

tan A = 12/5

To Find,

tan A/2 =?

Solution,

We know from the formula of tan θ, that

tan θ  = Perpendicular / Base

tan A = 12/5 = Perpendicular / Base

Therefore, Perpendicular = 12 and Base = 5

By using Pythagoras theorem,

Hypotenuse² = Perpendicular² + Base²

$H^2 = 12^2 + 5^2\\H^2 = 144 + 25\\H^2 = 169\\H = \sqrt{169}\\H = 13$

cos A = Base / Hypotenuse

cos A = 5 / 13

From the fomula of tan A / 2 we have,

$tan A / 2 = \sqrt{\frac{1 - cos A}{1 + cos A} }$

Putting the value of cos A in this equation,

$tan A / 2 = \sqrt{\frac{1 - 5 / 13}{1 +5 / 13} } \\tan A / 2 = \sqrt{\frac{(13 - 5)/ 13}{(13 + 5) / 13} } \\tan A / 2 = \sqrt{\frac{(13 - 5)}{(13 + 5)} } \\tan A / 2 = \sqrt{\frac{8}{18} } \\tan A / 2 = \sqrt{\frac{4}{9} } \\tan A / 2 = \frac{2}{3}$

tan A / 2 = 2 / 3

Hence, if tanA=12/5 then tanA/2​ is 2 / 3