(Q20)Simplify (1 – cos θ) (1 + cos θ) (1 + cot2 θ)

Given that

= (1 – cos θ) (1 + cos θ) (1 + cot2 θ)

= (1 – 2 θ) (1 + cot2 θ)

[∵ (a – b) (a + b) = a2 – b2]

= 2 θ. 2 θ

[∵ 1 – cos2 θ = sin2 θ; 1 + cot2 θ = cosec2 θ]

= 2 θ .
1
2 θ
[∵ cosec θ =
1
sin θ
]

=