(cot θ + tan θ)(cosec θ − sin θ)(cos θ − sec θ) = ________.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. -1.
We know,
cot A = cos A/sin A
tan A = sin A/cos A
cosec A = 1/sin A
sec A = 1/cos A
According to the question;
⇒ (cot θ + tan θ)(cosec θ − sin θ)(cos θ − sec θ)
⇒ [(cos θ/sin θ) + (sin θ/cos θ)]((1/sin θ) - sin θ)(cos θ - 1/cos θ)
⇒ ((cos2θ + sin2θ)/sin θ.cos θ)((1 - sin2θ)/sin θ)((cos2θ - 1)cos θ)
⇒ (1/sin θ.cos θ)(cos2θ/sin θ)(-sin2θ/cos θ)
⇒ -(sin2θ.cos2θ)/(sin2θ.cos2θ) = -1