Question

If $\sin \theta +\cos \theta =a$ and $\sec \theta +\csc \theta =b$, then the value of $b(a^2-1)$ is equal to

• A. $2a$
• B. $3a$
• C. $0$
• D. $2ab$

Answer 1

Answer: (A)

$2a$

$b(a^2-1)$
$=(\sec \theta +\csc \theta )\left[\right(\sin \theta +\cos \theta {)}^2-1]$
$=(\frac{1}{\cos \theta }+\frac{1}{\sin \theta })\left(2\sin \theta \cos \theta \right)$
$=2(\sin \theta +\cos \theta )=2a$