Question

Any one help me please

if A +B = 45 then prove that (1+tanA)(1+tanB) =2​

Answer 1

Step-by-step explanation:

Given :

A + B = 45

Now,

tan(A + B ) = 1 [•°• tan45° = 1 ]

By Using trigonometric identity for tan.

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

$\implies$ $\frac{TanA + tanB }{1 - tanAtanB}$ = 1

$\implies$ tanA + tanB = 1 - tanAtanB

$\implies$ tanA + tanB + tanAtanB = 1 .......(i)

Now ,

To prove : (1+tanA)(1+tanB) =2

Take L.H.S

$\implies$ (1+tanA)(1+tanB)

$\implies$ 1+ tanA + tanB +tanAtanB ....(ii)

Now put the value of expression from (i) in (ii)

$\implies$ 1+ (tanA + tanB +tanAtanB)

$\implies$ 1 + 1

= 2

L.H.S = R.H.S = 2

hence proved.