Q17 of 58 Page 8

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

Proof:


Taking LHS


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


Change all the trigonometric ratios into sin and cos terms.


We know,






=


[∵ (a – b) (a + b) = a2 – b2]



=



[∵sin2θ + cos2θ = 1]



=



= 2


= RHS


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