2025 · Q32
What is (1 + cot α−cosec α)(1 + tan α + sec α) equal to?
Elementary MathematicsTrigonometry
- A1/2
- B1
- C2
- D4
Explanation
Write 1 + cotα − cosecα = (sinα + cosα − 1)/sinα and 1 + tanα + secα = (sinα + cosα + 1)/cosα. Their product is ((sinα+cosα)² − 1)/(sinαcosα) = (2sinαcosα)/(sinαcosα) = 2, option (c).