Question

If cos theta=1/2 then tan theta/2

Answer 1

Answer:

cosθ

1

=2cosθ

2

cosθ

2

cosθ

1

=2

Applying componendo and dividendo, we get

cosθ

1

−cosθ

2

cosθ

1

+cosθ

2

=

2−1

2+1

⇒

−2sin(

2

θ

1

+θ

2

)sin(

2

θ

1

−θ

2

)

2cos(

2

θ

1

+θ

2

)cos(

2

θ

1

−θ

2

)

=3

⇒tan(

2

θ

1

+θ

2

)tan(

2

θ

1

−θ

2

)=−

3

1