Question

if 7sinA -7sinB =9cosA-9cosB then prove 16tan(A+B)=63

Answer 1

Step-by-step explanation:

Given---> 7SinA - 7SinB = 9CosA - 9 CosB

To prove----> 16 tan(A + B ) = 63

Solution----->

1) Plzz see the attachment.

2) In third step we apply two formulee,

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

CosA - CosB = - 2 Sin{(A+B)/2} Sin{(A-B)/2}

3) In 6th step , we use formula given below

Sinθ / Cosθ = tanθ

4) then we apply ,

tan2θ = 2tanθ / ( 1 - tan²θ )

and putting θ = ( A + B ) / 2