Question

WHAT IS THE FORMULA OF TAN 3X​

Answer 1

Answer:

In general, we know that

tan(A+B+C)=tanA+tanB+tanC−tanAtanBtanC1−tanAtanB−tanBtanC−tanCtanA

Now, setting A=B=C=x in above trigonometric identity, we get

tan(x+x+x)=tanx+tanx+tanx−tanxtanxtanx1−tanxtanx−tanxtanx−tanxtanx

tan3x=3tanx−tan3x1−3tan2x

Method 2:

We know that

tan(A+B)=tanA+tanB1−tanAtanB

∴tan3x

=tan(x+2x)

=tanx+tan2x1−tanxtan2x

=tanx+tan(x+x)1−tanxtan(x+x)

=tanx+tanx+tanx1−tanxtanx1−tanxtanx+tanx1−tanxtanx

=tanx+2tanx1−tan2x1−2tan2x1−tan2x

=tanx−tan3x+2tanx1−tan2x1−tan2x−2tan2x1−tan2x

=3tanx−tan3x1−3tan2x

Answer 2

Answer:

$3 \tan(x) = 3 \tan(x) - { \tan }^{3} x \div 1 - 3 { tan }^{2} x$