Q.44 \lim _{x \rightarrow 0} \frac{\cos 7 x^{\circ}-\cos 2 x^{\circ}}{x^{2}} is
A. \frac{-45}{2} \pi^{2}
B. \frac{-45}{2} \pi
C. \frac{-\pi^{2}}{1440}
D. \frac{-\pi^{2}}{2880}
Answer: C \frac{-\pi^{2}}{1440}
Explanation
\lim _{x \rightarrow 0} \frac{\cos 7 x^{\circ}-\cos 2 x^{\circ}}{x^{2}} =\lim _{x \rightarrow 0} \frac{\cos \left(\frac{7 \pi}{180}\right) x-\cos \left(\frac{2 \pi}{180}\right) x}{x^{2}} =\frac{\left(\frac{2 \pi}{180}\right)^{2}-\left(\frac{7 \pi}{180}\right)^{2}}{2} =\frac{-\pi^{2}}{1440} \because \lim _{x \rightarrow 0} \frac{\cos m x-\cos n x}{x^{2}}=\frac{n^{2}-m^{2}}{2}