Question

if tan (a+b)=root 3 & tan (a-b)=0,find sin(a+b) and cos (a-b).

Answer 1

Answer:

Given tan(A+B)=

3

⟹A+B=60

∘

⋯(1)

tan(A−B)=

3

1

⟹A−B=30

∘

⋯(2)

(1)+(2)⟹2A=90

∘

⟹A=45

∘

Put A value in (1)

⟹B=60

∘

−45

∘

=15

∘

Answer 2

given that

Tan (A+B) =√3

but we know that tan 60=√3

Thus

Tan ( A+B) = tan 60

A+B =60

Tan (A–B) =1/√3

but we know that

Tan 30 1/√3

Thus

Tan ( A–B) = tan 30

A– B=30