Question

 if cosec theta-cot theta= alpha ​

Answer 1

Step-by-step explanation:

cosecθ−cotθ=x

sinθ

1

−

sinθ

cosθ

=x

sinθ

1−cosθ

=x

sinθ

1−cosθ

(1+cosθ)

(1+cosθ)

=x

sinθ(1+cosθ)

1−cos

2

θ

=x

sinθ(1+cosθ)

sin

2

θ

=x

1+cosθ

sinθ

=x

sinθ

1+cosθ

=

x

1

(1)

Now

cosecθ+cotθ=

sinθ

1

+

sinθ

cosθ

=

sinθ

1+cosθ

=

x

1

Hence cosecθ+cotθ=

x

1