Question

Show that (cosec∅-cot∅)²=1-cos∅/1+cos∅.​

Answer 1

Answer:

We have,

(cosecθ−cotθ)

2

=(

sinθ

1

−

sinθ

cos θ

)

2

=(

sinθ

1−cosθ

)

2

=

sin

2

θ

(1−cosθ)

2

=

1−cos

2

θ

(1−cosθ)

2

[∵sin

2

θ=1−cos

2

θ]

=

(1−cosθ)(1+cosθ)

(1−cosθ)

2

=

1+cosθ

1−cosθ