Solve the following:
(tanθ + secθ + 1)(cotθ - cosecθ + 1) = ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 2.
According to the given question,
(tanθ + secθ + 1)(cotθ - cosecθ + 1)
⇒ (sinθ/cosθ + 1/cosθ + 1)(cosθ/sinθ - 1/sinθ + 1)
⇒ ((sinθ + 1 + cosθ)/cosθ)((cosθ - 1 + sinθ)/sinθ)
⇒ (sinθcosθ - sinθ + sin2θ + cosθ - 1 + sinθ + cos2θ - cosθ + cosθsinθ)/cosθsinθ
⇒ (2sinθcosθ + 1 - 1)/sinθcosθ
⇒ 2sinθcosθ/sinθcosθ = 2
Hence the required answer is 2.