Question

Period of cot $\cos(4x + 3)$ is.

• A. $\frac{\pi}{2}$
• B. $\pi$
• C. $2\sin 3\theta$
• D. $\frac{2\pi}{3}$

Answer 1

Answer: (C)

$2\sin 3\theta$

Answer 2

Period of $a + c - 3b = 0$ is $\frac{\sin\frac{A}{2}\sin\frac{C}{2}}{\sin\frac{B}{2}} = \sqrt{\frac{ac(s - b)(s - c)(s - b)(s - a)}{(s - a)(s - c)bc \times ab}} = \frac{s - b}{b}$ and period of $2b = a + c$ is $\frac{s - b}{b} = \frac{\frac{3b}{2} - b}{b} = \frac{1}{2}$ $\tan\frac{B - C}{2} = x\cot\frac{A}{2} \Rightarrow x = \frac{b - c}{b + c}$ L.C.M. is $\cos B = \frac{9 + 25 - 16}{2.3.5} = \frac{18}{2.3.5} = \frac{3}{5} \Rightarrow \sin B = \frac{4}{5}$.