Question
Download Solution PDFSolve the following: (tan θ + sec θ + 1)(cot θ - cosec θ + 1) = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
(tan θ + sec θ + 1)(cot θ - cosec θ + 1) = ?
Formula Used:
tan θ = sin θ / cos θ
sec θ = 1 / cos θ
cot θ = cos θ / sin θ
cosec θ = 1 / sin θ
Calculation:
(tan θ + sec θ + 1)(cot θ - cosec θ + 1)
⇒ (sin θ / cos θ + 1 / cos θ + 1)(cos θ / sin θ - 1 / sin θ + 1)
⇒ ( (sin θ + 1 + cos θ) / cos θ ) ( (cos θ - 1 + sin θ) / sin θ )
⇒ ( (sin θ + 1 + cos θ) / cos θ ) ( (cos θ + sin θ - 1) / sin θ )
⇒ (sin θ + 1 + cos θ)(cos θ + sin θ - 1) / (cos θ sin θ)
⇒ (sin θ + cos θ + 1)(sin θ + cos θ - 1) / (cos θ sin θ)
⇒ ((sin θ + cos θ)2 - 1) / (cos θ sin θ)
⇒ (sin2 θ + cos2 θ + 2sin θ cos θ - 1) / (cos θ sin θ)
⇒ (1 + 2sin θ cos θ - 1) / (cos θ sin θ)
⇒ (2sin θ cos θ) / (cos θ sin θ)
⇒ 2
∴ The correct answer is option 2.
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