$Quad-Trigonometry$

Algebra Level 3

if ${ a }^{ 2 }-2a\cos { x } +1=674$ and $\tan { \frac { x }{ 2 } } =7\quad$ then integral value of a is :

1 solution

Vishal Choudhary
May 16, 2014

from trigonometry we have.

cosx=(1-tanx/2^2)/(1+tanx/2^2)

we get cosx=-48/50

our equation becomes

a^2 + 48/25a - 673=0

on factorizing.

1/25(x-25)(25x+673)=0

since we want the integral solution

required answer is 25