Question

Verify that tan30°=tan60°-tan30°/1+tan60°×tan30°

Answer 1

tan60°-tan30°/1+tan60°-tan30°
It is in the form of

(tanA - tanB)/(1 - tanA ×tanB) =tan(A - B)

Hence
tan60°-tan30°/1+tan60°tan30° = tan(60° − 30°) = tan(30°) =1/√3

With out formula we can done it is given

tan60=√3
tan30=1/√3

So our expression become
= (√3- 1/√3)/(1+(√3 ×1/√3))

=(√3-1/√3)/1+1

=((√3×√3-1)/√3)/2

=((3-1)/√3))/2

=(2/√3)/2

=1/√3 = tan30