Question

If $\sin \theta +\cos \theta =m$ and $\sec \theta +\cos ec\theta =n,$ then $n(m+1)(m-1)=?$

• A. $m$
• B. $n$
• C. $2m$
• D. $2n$

Answer 1

The correct option is C $2m$

$m=\sin \theta +\cos \theta ⟹m^2={\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =1+2\sin \theta \cos \theta$

$⟹\sin \theta \cos \theta =\frac{m^2-1}{2}$

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

$⟹n(m^2-1)=2m⟹n(m+1)(m-1)=2m$