Question

If cosA+cosB=1/3
sinA+sinB=1/4
Prove that-tan(A+B)/2=3/4​

Answer 1

Answer:

Step-by-step explanation:

CosA + CosB = 1/3

SinA + SinB = 1/4

But,

CosA + CosB = 2Cos(A+B)/2.Cos(A-B)/2  --- (1)

SinA + SinB = 2Sin(A+B)/2.Cos(A-B)/2  --- (2)

Divide (2) by 1

SinA + SinB / CosA + CosB = (1/4) / (1/3)

=> 2Sin(A+B)/2.Cos(A-B)/2 / 2Cos(A+B)/2.Cos(A-B)/2 = 1/4 * 3/1

=> Sin(A+B)/2 / Cos(A+B)/2 = 3/4

=> Tan(A+B)/2 = 3/4

Hence proved.