2022 · Q57
Consider the following :
- 1√(sec²θ + cosec²θ ) = tanθ +cotθ where 0° < θ < 90°. √(tan²θ + cot²θ + 4) = secθ +cosec θ where 0° < θ < 90°.
Which of the above is/are an identity/identities?
Elementary MathematicsTrigonometry
- A1 only
- B2 only
- CBoth 1 and 2
- Dneither 1 nor 2
Explanation
√(sec²θ+cosec²θ) = √(2+tan²θ+cot²θ) = tanθ+cotθ (positive for acute θ), so statement 1 is an identity. Statement 2 would require secθcosecθ = 1, i.e. sin2θ = 2, impossible - not an identity. Hence the keyed option is A.