Question

A+B+C=180 AND COS A=COS B COS C THEN FIND TAN A

Answer 1

A+B+C=180 AND COS A=COS B COS C THEN FIND TAN A

Step-by-step explanation:

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)] ———-(x)

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 ———(y)

From (x) and (y) above we get :

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

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