Question

A+B+C=180 & cos A = cos B*cos C Prove that Tan B*Tan C=2​

Answer 1

Answer:

As we know,

Sin(π - A) = Sin(A)

Cos(π - A) = Cos(A)

Tan(π - A) = Tan(A)

As A+ B + C = 180

=> A = 180 - (B + C)

So Tan(A) = Tan(180 - (B + C))

= Tan(B + C)

= [ Tan(B)+ Tan(C)]/ [ 1 - Tan(B).Tan(C)] ———-(1)

As, Cos(A) = Cos(B).Cos(C)

=> Cos(180 - (B+C)) = Cos(B).Cos(C)

=> Cos(B+C) = Cos(B).Cos(C)

=> Cos(B).Cos(C) - Sin(B).Sin(C) = Cos(B).Cos(C)

=> Sin(B).Sin(C) = 0

=> Tan(B).Tan(C) = 0 ———(2)

From (1) and (2)

Tan(A) = Tan(B)+ Tan(C)

Step-by-step explanation: