Prove that

OR

Prove that (1 + cot θ - cosec θ) (1 + tan θ + sec θ) = 2

L.H.S:

Hence, Proved!

OR

Taking LHS

(1 + cot θ - cosec θ) (1 + tan θ + sec θ)

Change all the trigonometric ratios in terms of sin and cos

We know,

[∵ (a – b) (a + b) = a² – b²]

[∵sin²θ + cos²θ = 1]

= 2 = RHS

Hence, proved.