Question

What is the value of tan20 + tan40 + tan60+ tan 80 + .....+tan160

Answer 1

Final Answer : 0

Understanding:
1) tan(180°-α) = -tan(α)


Steps:
tan(20°) + tan(40°) + tan(60°) + .....+ tan( 160°)
=> tan(20°) + tan(40°) +.......-tan(40°) - tan(20°)
=> Since, these are even no. of terms (160/20=8)
all will be paired and will get cancelled out.
=> (tan20°) -tan(20°) + tan(40°) - tan(40°) +....
=> 0 +0 +..
=>0.