Question-1 The complete solution set of equation (5+4\cos\theta)(2\cos\theta+1)=0 in the interval \lbrack0,2\pi\rbrack
A) \left\{\frac{\pi}{3},\frac{2\pi}{3}\right\}
B) \left\{\frac\pi3,\pi\right\}
C) \left\{\frac{2\pi}4,\frac{4\pi}3\right\}
D) \left\{\frac{2\pi}3,\frac{5\pi}3\right\}
Answer: C)
Explanation
Given equation is
(5+4\cos\theta)(2\cos\theta+1)=05+4\cos\theta=0 or 2\cos\theta+1=0
\Rightarrow\cos\theta=\frac{-5}4 or \cos\theta=\frac{-1}2
\Rightarrow\cos\theta=\frac{-1}2(\because-1\leq\cos\theta\leq1) \ln\lbrack0,2\pi\rbrack,\theta=\frac{2\pi}3,\frac{4\pi}3