Question

Prove that tan 8 − tan 5 − tan 3 = tan 8 .tan 5 .tan 3​

Answer 1

Step-by-step explanation:

We know 5+3=8

Apply tan on both sides

tan(5+3)=tan(8)

tan 5+tan3/[1-tan5tan3]=tan8

tan5+tan3=tan8-tan5tan3tan8

tan8tan5tan3=tan8-tan5-tan3

Answer 2

Step-by-step explanation:

tan(A+B)=1−tanAtanB/tanA+tanB

⇒tanA+tanB=tan(A+B)(1−tanAtanB)

∴L.H.S=tan8θ−tan5θ−tan3θ

=tan8θ−(tan5θ+tan3θ)

=tan8θ−[tan(5θ+3θ)(1−tan5θtan3θ)]

=tan8θ−[tan8θ(1−tan5θtan3θ)]

=tan8θ−(tan8θ−tan8θtan5θtan3θ)

=tan8θ−tan8θ+tan8θtan5θtan3θ

=0+tan8θtan5θtan3θ