Question

If A+B=225, then what is the value of (1+tan A)(1+tan B)?

Answer 1

A+B=225=180+45 i.e tan(A+B)=tan (180+45) i.e. tan(A+B)=tan45 i.e tan(A+B)= 1 i.e. (tanA+tanB)/(1-tanAtanB)=1 i.e. tanA+tanB=1-tanAtanB i.e. tanA+tanB+tanAtanB=1 i.e. 1+tanA+tanB+tanAtanB=1+1=2 i.e. (1+tanA)(1+tanB)=2

Answer 2

Step-by-step explanation:

Given A + B = 225.

         Multiply with tan on both sides, we get

Tan(A + B) = tan 225

Tan(A + B) = tan(180 + 45)

Tan(A + B) = Tan 45

Tan(A + B) = 1.

Tan A + Tan B/1 - Tan A Tan B = 1

Tan A + Tan B = 1 - Tan A Tan B

Tan A + Tan B + Tan A Tan B = 1   -------- (1)

Given (1 + Tan A)(1 + Tan B)

          = 1 + Tan B + Tan A + Tan A Tan B

          = 1 + 1

          = 2.

Therefore (1 + Tan A)(1 + Tan B) = 2.

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