Question

tan (A+B) =1/2 and tan(A-B) = 1/3 then find the value of tan (2A)

Answer 1

Hi ,

Tan(A+B)= 1/2 ---( 1 )

Tan(A -B) = 1/3-----( 2 )

Tan(2A)

=Tan[(A+B)+(A-B)]

=[Tan(A+B)+Tan(A-B)]/[1-tan(A+B)tan(A-B)]

= [1/2+1/3]/[1-1/2×1/3]

=[(3+2)/6]/[(6-1)/6]

=[5/6]/[5/6]

= 1

Therefore,

Tan 2A = 1

I hope this helps you.

:)

Answer 2

Answer:

1/√2

Step-by-step explanation:

tan (A+B)=3

tan(A=B)=2

tan[(A+B)+(A-B)]=(3+2)/1-6=-1

tan 2A=-1

sin 2A=-1/√2

but 1 quadrant which means all angles would be positive

hence sin2A=1/√2