Question

If tan(theta/2)=5/2 and tan(phi/2)=3/4 then find value of cos(theta+phi)

Answer 1

Given,

Tan (θ/2) = 5/2;

Tan (ϕ/2) = 3/4;

Now,

We know that, Tan (A+B) = (Tan A + Tan B) / (1 + Tan A x Tan B);

So,

Tan (θ/2 + ϕ/2) = (Tan θ/2 + Tan ϕ/2 ) / (1 + (Tan θ/2 x Tan ϕ/2) );

Tan (θ/2 + ϕ/2) = (5/2 + 3/4) / (1 + (5/2 x 3/4) );

Tan (θ/2 + ϕ/2) = (13/4) / (1 + 15/8);

Tan (θ/2 + ϕ/2) = (13/4) / (23/8);

Tan (θ/2 + ϕ/2) = 26/23;

(θ/2 + ϕ/2) = Tan-1(26/23);

Θ + ϕ = 2 Tan-1(26/23);

So,

Cos (Θ + ϕ) = Cos (2 Tan-1(26/23) );

Answer 2

Answer:

Ans: -627/725

Step-by-step explanation: