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If cos θ + sin θ = m and sec θ + cosec θ = n then the value of n (m² – 1) is equal to :
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- 2m
- mn
- 4mn
- 2n
Correct Option: A
cosθ + sinθ = m --- (i)
secθ + cosecθ = n
| ⇒ | + | = n | cosθ | sinθ |
| ⇒ | = n --- (ii) | sinθ . cosθ |
| ∴ n (m² – 1) = | sinθ . cosθ |
[(sinθ + cosθ)² – 1]
| = | (sin²θ + cos²θ + 2sinθ cosθ – 1) | sinθ . cosθ |
| = | × 2sinθ . cosθ | sinθ . cosθ |
[∵sin²θ + cos²θ = 1]
= 2 (sinθ + cosθ) = 2m
