The value of (1 + tan 10°)(1 + tan35°) is :

We know,

If A + B = 90°

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

Now,

( 1 + tan10° ).(1 + tan35° )

As ,

Sum of angle is 10° + 35° = 45°

So,

( 1 + tan10° ).(1 + tan35° )

= 2