67
The maximum distance of a point on the graph of the function $y=\sqrt{3} \sin x+\cos x$ from $X$-axis is ......... .
Explanation
Given that, $y=\sqrt{3} \sin x+\cos x$
$$\begin{aligned} y & =2\left[\frac{\sqrt{3}}{2} \sin x+\frac{1}{2} \cos x\right] \\ & =2\left[\sin x \cdot \cos \frac{\pi}{6}+\cos x \sin \frac{\pi}{6}\right] \\ & =2 \sin (x+\pi / 6) \end{aligned}$$
Graph of $y=2\sin x$
Hence, the maximum distance is 2 units.
68
In each of the questions 68 to 75 , state whether the statements is True or False? Also, give justification.
A
TRUE
B
FALSE
69
The equality $\sin A+\sin 2 A+\sin 3 A=3$ holds for some real value of $A$.
A
TRUE
B
FALSE
70
$\sin10\Upsilon$ is greater than $\cos10\Upsilon$.
A
TRUE
B
FALSE
71
$\cos \frac{2 \pi}{15} \cos \frac{4 \pi}{15} \cos \frac{8 \pi}{15} \cos \frac{16 \pi}{15}=\frac{1}{16}$
A
TRUE
B
FALSE