Question

If tan =

sin cos
/1− 2

, show that tan ( − ) = (1 – n) tan .​

Answer 1

Step-by-step explanation:

ANSWER

tanβ=

1−nsin

2

α

nsinαcosα

=

sec

2

α−ntan

2

α

ntanα

=

1+tan

2

α−ntan

2

α

ntanα

=

1+(1−n)tan

2

α

ntanα

∴tan(α−β)=

1−tanαtanβ

tanα−tanβ

=

1−

1−tanαtanβ

tanαntanβ

tanα−

1+(1−n)tan

2

α

ntanα

=(1−n)tanα