Question

$tan theta = \sqrt{3} \:and \: tan \: pie = 2 - \sqrt{3 \: } show \: that \: \: theta - pie = \pi \div 4$
​

Answer 1

Answer:

Answer

The given equation can be written as

tanx+

1−tanxtan

3

π

tanx+tan

3

π

+

1−tanxtan

3

2π

tanx+tan

3

2π

=3

⇒tanx+

1−

3

tanx

tanx+

3

+

1+

3

tanx

tanx−

3

=3

⇒tanx+

1−3tan

2

x

8tanx

=3

⇒

1−3tan

2

x

tanx(1−3tan

2

x)+8tanx

=3

⇒

1−3tan

2

x

3(3tanx−tan

3

x)

=3

⇒3tan3x=3⇒tan3x=1

⇒3tan3x=3⇒tan3x=1

⇒3x=nπ+

4

π

⇒x=

3

nπ

+

12

π