Question

prove that 3 tan-1 x + cot-1 x = Π​

Answer 1

Step-by-step explanation:

We have, 3tan

−1

x+cot

−1

x=π

⇒2tan

−1

x+(tan

−1

x+cot

−1

x)=π

⇒2tan

−1

x+

2

π

=π, [∵tan

−1

x+cot

−1

x=

2

π

] is an identity

⇒2tan

−1

x=π−

2

π

=

2

π

⇒tan

−1

x=

4

π

∴x=tan

4

π

=1

Answer 2

Answer:

We have, 3tan

−1

x+cot

−1

x=π

⇒2tan

−1

x+(tan

−1

x+cot

−1

x)=π

⇒2tan

−1

x+

2

π

=π, [∵tan

−1

x+cot

−1

x=

2

π

] is an identity

⇒2tan

−1

x=π−

2

π

=

2

π

⇒tan

−1

x=

4

π

∴x=tan

4

π

=1