Question

If $\sin\theta + \cos\theta = m$and $\sec\theta + \text{cosec}\theta = n$, the$n(m + 1)(m - 1) =$

• A. m
• B. n
• C. 2m
• D. 2n

Answer 1

Answer: (C)

2m

Answer 2

$n(m^{2} - 1) = (\sec\theta + \text{cosec}\theta).2\sin\theta\cos\theta$

($\because m^{2} = 1 + 2\sin\theta\cos\theta$)

$= \frac{\sin\theta + \cos\theta}{\sin\theta.\cos\theta}.2\sin\theta\cos\theta = 2m$.