Question

tan10+tan35+tan10×tan35?

Answer 1

tan10° + tan35° + tan10°.tan35° = ?

tan45° = tan(10° + 35°)
we know,
$tan(A+B)=\frac{tanA+tanB}{1-tanA.tanB}$
so, tan45° = (tan10° + tan35°)/(1-tan10°.tan35°)
1 = (tan10° + tan35°)/(1-tan10°.tan35°)
1 - tan10°.tan35° = tan10° + tan35°
1 =tan10° + tan35° + tan10°.tan35°

hence, tan10° + tan35° + tan10°.tan35° = 1