Question

tan66° + tan69°\1- tan66°.tan69°

Answer 1

tan66°+tan69°-tan66°.tan69°

$tan(a + b) = \frac{tana + tanb}{1 - tanatanb}$

66°+69°=135°

applying tan on both sides

tan(66°+69°)=tan135°

tan135°=tan(90°+45°)

Tan(90°+theta )lies in 2nd quadrant

in 2nd quadrant tan is negative

so,tan135°=-tan45°

tan45°=1

-tan45°=-1

tan135°=-1

tan66°+tan69°/1-tan66°tan69°=-1

so,tan66°+tan69°/1-tan66°tan69°=1