Question

What is the value of tan 20° + tan 40° + √3 tan20° tan40°?

Answer 1

we know, tan(A + B) = (tanA + tanB)/(1 - tanA.tanB)

tan60° = tan(20° + 40°)

or, √3 = (tan20° + tan40°)/(1 - tan20°. tan40°)

or, √3(1 - tan20° . tan40°) = tan20° + tan40°

or, √3 - √3 . tan20° . tan40° = tan20° + tan40°

or, √3 = tan20° + tan40° + √3tan20°. tan40°


hence, tan20° + tan40° + √3tan20°. tan40° = √3

Answer 2

HELLO DEAR,



we know:-
tan(A + B) = (tanA + tanB)/(1 - tanA.tanB)

now,
tan60° = tan(20° + 40°)

=> √3 = (tan20° + tan40°)/(1 - tan20°. tan40°)

=> √3(1 - tan20° . tan40°) = tan20° + tan40°

=> √3 - √3 . tan20° . tan40° = tan20° + tan40°

=> √3 = tan20° + tan40° + √3tan20°. tan40°


hence,
tan20° + tan40° + √3tan20°. tan40° = √3


I HOPE IT'S HELP YOU DEAR,
THANKS