Question

Help me solve this question.

Answer 1

Things to know:

1) Let α =a and β = b .
sin a = 2tan (a/2)/(1+tan^2(a/2) )

cos a = [1- tan^2(a/2)] / [1+tan^2(a/2)]

2) cos (a + b ) = cos a cos b - sin a sin b

Steps :
1) First find roots of the quadratic equation .
(shown in pic 1)
2) There are two cases available for two roots .
Case 1: When tan (a/2) = 5/2 and tan( b/2) = 3/4 .(shown in pic 1)

Case 2: When tan (a/2) = 3/4 and tan (b/2) = 5/2
( This will also give same answer )

Final result :
cos (a + b) = -627/725


Hope , you understand my answer and it may help you!