Question

If A + B = 450, then prove that (1 + tanA) (1 + tanB) = 2.
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Answer 1

Answer:

To prove (1+Tan A ) (1 + tan B ) =×

Step-by-step explanation:

taking l.h.s.

tan( A+ B)= tan A + tan B/1- tanAtanB

= tan45°=tanA+tanB/1-tanAtanB

=1-tanAtanB=tanA+tanB

=2=1+tanA+tanB+tanAtanB

=2=(1+tanA)(1+tanB)

Hence Proved

Answer 2

Answer:

Given,

A + B = 45°

apply tan on both sides

tan(A+B)=tan45°

w.k.t(we know that)

$tan(A+B)=\frac{tanA+tanB}{1-tanAtanB}$

So,

$\frac{tanA+tanB}{1-tanAtanB}=tan45\\\frac{tanA+tanB}{1-tanAtanB}=1$                                       [tan45°=1]

now cross multiply

tanA+tanB=1-tanAtanB

tanA+tanAtanB+tanB=1

tanB+tanA(1+tanB)=1

now,

add 1 on both sides

1+tanB+tanA(1+tanB)=1+1

1(1+tanB)+tanA(1+tanB)=2

(1+tanA)(1+tanB)=2

∴Hence prove