Question

Which one of the following equations has no solution?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

(a) $cosec\theta –\sec \theta =cosec\theta \sec \theta$
$\Rightarrow \frac{\cos \theta -\sin \theta }{\cos \theta \sin \theta }=\frac{1}{\cos \theta \sin \theta }$
$\Rightarrow \cos \theta =1+\sin \theta$
Provided that $\sin 2\theta \ne 0$
No $\theta$ satisfies above relation.

(b) $cosec\theta .\sec \theta =1$
$\Rightarrow \sin \theta \cos \theta =1$
$\Rightarrow \sin 2\theta =2$ (not possible)

(c) $\cos \theta +\sin v=\sqrt{2}$
$\Rightarrow (\theta -\frac{\pi }{4})=1$
$\therefore$ Solution exists.

(d) $\sqrt{3}\sin \theta -\cos \theta =2$
$\Rightarrow \sin (\theta -\frac{\pi }{3})=1$
$\therefore$ Solution exists.