Question

If $\sin \theta +\cos \theta =m$ and $\sec \theta +\text{cosec}\theta =n$, then

• A. $2n=m\left(n^2-1\right)$
• B. $2m=n\left(m^2-1\right)$
• C. $2n=m\left(m^2-1\right)$
• D. $2m=n^2(n-1)$

Answer 1

Answer: (B)

$\sin \theta +\cos \theta =m$ ....(1)
$\sin \theta \cos \theta =m/n$.....(2)
squaring (1)
$1+2\sin \theta \cos \theta =m^2$
$\sin \theta \cos \theta =\frac{m^2-1}{2}$......(3)
by $(2)\&(3)n\left(m^2-1\right)=2m$