2020 · Q47
If cos θ + sec θ = k, then what is the value of sin²θ − tan²θ?
Elementary MathematicsTrigonometry
- A4 − k
- B4 − k²
- Ck² − 4
- Dk² + 2
Explanation
Put u = cos^2(theta); then (u+1)^2 = k^2*u. Now sin^2(theta)-tan^2(theta) = -(1-u)^2/u = -((k^2-4)u)/u = 4-k^2. Hence option (B).