Question

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

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

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 $(2) \&(3) n\left(m^2-1\right)=2 m$