Question

tan(60°+a)tan(60°-a) is equal to​

Answer 1

Answer:

Correct option is

A 3 tan 3A

tan(60+ A)=

1−tan60

o

tanA

tan60

o

+tanA

=

1−

3

tanA

3

+tanA

tan(60− A)=

1+tan60

o

tanA

tan60

o

−tanA

=

1+

3

tanA

3

−tanA

tan(60+A)−

tan(60−

A)=

1−

3

tanA

3

+tanA

−

1+

3

tanA

3

−tanA

=

1 2

3

tanA)

2

(

3

+tanA)(1+

3

tanA)−(

3

−tanA)(1−

3

tanA)

=

1−3tan

2

A

3

+3tanA+tanA+

3

tan 2

3

+3tanA+tanA−

3

tan 2

=

1−3tan

2

A

8tanA

tanA+ tan(60+ A)− tan(60− A)= tanA+

1−3tan

2

A

8tanA

=

1−3tan

2

A

tanA−3tan

3

A+8tanA

=

1−3tan

2

A

3(3tanA−tan

3

A)

= 3tan3A

(∵tan3A=

1−3tan

2

A

3tanA−tan

3

A

).