Question
Class 11MathematicsTrigonometric Functions

Prove that: tanα tan(60° - α) tan(60° + α) = tan3α

Verified Answer

Prove that

tan α tan (60° - α) tan (60° + α) = tan3α

L.H.S. = tan α tan (60° - α) tan (60° + α)

= tan α (tan 60° - tan α)/(1 + tan 60° tan α) (tan 60° + tan α)/(1 - tan 60° tan α)

= tan α (√3 - tan α)/(1 + √3 tan α) (√3 + tan α)/(1 - √3 tan α)

= tan α (3 - tan2α)/(1 - 3 tan2α)

= (3 tan α - tan3α)/(1 - 3 tan2α)= tan 3α R.H.S.