Q. The equation $a\cos{\theta + b\sin{\theta = c}}$ has a solution, when $a,\ b$ and $c$ are real numbers such that
A) $a < b < c$
B) $a = b = c$
C) $c^{2} \leq a^{2} + b^{2}$
D) $a^{2} \leq a^{2} - b^{2}$
Explanation
(c)
The given equation is
$a\cos{\theta + b\sin{\theta = c}}$
Since, $\sqrt{a^{2} - b^{2}} \leq a\cos{\theta + b\sin{\theta \leq \sqrt{a^{2} + b^{2}}}}$
$\Rightarrow c^{2} \leq a^{2} + b^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.