Question

1-tan A tan B/1+tan A tan B =cos (A + B) -cos (A - B) prove it​

Answer 1

Step-by-step explanation:

We need to prove this

( 1 - Tan(A).Tan(B))/(1 + Tan(A).Tan(B)) = Cos(A + B)/Cos(A - B)

Solving the LHS :

( 1 - Tan(A).Tan(B))/(1 + Tan(A).Tan(B))

=> ( 1 - (Sin(A).Sin(B))/Cos(A).Cos(B)) / (1 + (Sin(A).Sin(B))/Cos(A).Cos(B))

Now multiplying each identity by Cos(A).Cos(B)

=> (Cos(A).Cos(B) - Sin(A).Sin(B)) / (Cos(A).Cos(B) + Sin(A).Sin(B))

Now by using identities :

Cos(A).Cos(B) - Sin(A).Sin(B) = Cos(A + B)

and

Cos(A).Cos(B) + Sin(A).Sin(B) = Cos(A - B)

=> Cos(A + B)/Cos(A - B)

Hence , proved , LHS = RHS