Find the value of (cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ).
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 1.
(cosec θ - sin θ )(sec θ - cos θ )(tan θ + cot θ )
⇒ (1/sin θ - sin θ)(1/cos θ - cos θ)(sin θ/cos θ + cos θ/sin θ)
⇒ [(1 - sin2 θ)/sin θ][(1 - cos2 θ)/cos θ)][(sin2 θ + cos2 θ)/(sin θ cos θ)]
⇒ (cos2 θ/sin θ)(sin2 θ/cos θ)[1/(sin θ cos θ)] [∵ sin2 θ + cos2 θ = 1]
⇒ (cos2 θ sin2 θ)/(sin2 θ cos2 θ)
⇒ 1
Therefore, the value of the given expression is 1.