Question

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

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

Answer 1

The correct option is A $2a$

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

Therefore, Answer is $2a$