Question

A plus b is 225 .find (1plus tan a)(1 plus tan b)

Answer 1

Hi ,

It is given that ,

A + B = 225

tan( A+ B ) = tan 225

[ ( tanA + tanB )/(1-tanAtanB) = tan ( 180 + 45 )

tanA+tanB = tan 45 ( 1 - tanAtanB )

tanA + tanB = 1 - tanAtanB

tanA + tanB + tanAtanB = 1

tanA + tanAtanB + tanB = 1

tanA ( 1 + tan B ) + tanB = 1

add 1 bothsides of the equation , we get

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

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

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


Therefore ,

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

I hope this helps you.

: )

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.

Hope it's help you..