Question

A+B=135º then (1-tan A)(1-tanB)=
1) 1
2) 2
3) -1
4) 4
​

Answer 1

Solution :-

Given

• A + B = 135°

We know

$\star\sf{\dfrac{tan A + tanB}{1-tan.AtanB} = tan(A+B) }$

$\star\sf{ tan135^{\circ} = -1}$

From this

$\implies \sf{\dfrac{tan A + tanB}{1-tanA.tanB} = -1 }$

$\implies \sf{tan A + tanB = -(1-tanA.tanB) }$

Now our term

= (1 - tanA )( 1 - tanB)

= 1 - (tanA + tanB ) + tanA.tanB

Replace ( tanA + tanB )

= 1 - (-)(1 - tanA.tanB) + tanA.tanB

= 1 + 1 - tanA.tanB + tanA.tanB

= 2