Question

Tana=1/3 anf tanb=1/2 prove that sin2(A+B)=1

Answer 1

you can apply the formula tan(A+B) and sin(A+B)

Answer 2

we know that sin2a = 2tana/1+tan²a

so

sin2(a+b)=2tan(a+b)/1+tan²(a+b)

tana+b =(1/2+1/3) /1-1/2*1/3
i.e. 1
tan²(a+b) is 1

putting all values

2*1/1+1
=1 thus proved