Chapter 11, Problem 8STP

To determine

To evaluate: the option which is not a solution of $2\sin 2x\cos x=-\cos x$ .

Answer to Problem 8STP

Option B, C and D are not the solution of given equation.

Explanation of Solution

Given:

  $2\sin 2x\cos x=-\cos x$

Calculation: -

Putting the options one by one,

Checking option A,

Taking left hand side,

  $\begin{array}{l}2\sin 2x\cos x=2\sin \pi \cos \frac{\pi }{2}\\ 2\sin \pi \cos \frac{\pi }{2}=0\end{array}$

Taking the right hand side,

  $\begin{array}{c}-\cos x=-\cos \frac{\pi }{2}\\ =0\end{array}$

So, option A is the solution of given equation.

Checking option B,

Taking left hand side,

  $\begin{array}{l}2\sin 2x\cos x=2\sin \frac{7\pi }{6}\cos \frac{7\pi }{12}\\ 2\sin \frac{7\pi }{6}\cos \frac{7\pi }{12}=0.126\end{array}$

Taking the right hand side,

  $\begin{array}{c}-\cos x=-\cos \frac{7\pi }{12}\\ =-0.999\end{array}$

So, option B is not the solution of given equation.

Checking option C,

Taking left hand side,

  $\begin{array}{l}2\sin 2x\cos x=2\sin \frac{11\pi }{6}\cos \frac{11\pi }{12}\\ 2\sin \frac{11\pi }{6}\cos \frac{11\pi }{12}=0.1997\end{array}$

Taking the right hand side,

  $\begin{array}{c}-\cos x=-\cos \frac{11\pi }{12}\\ =-0.999\end{array}$

So, option C is not the solution of given equation.

Checking option D,

Taking left hand side,

  $\begin{array}{l}2\sin 2x\cos x=2\sin \frac{7\pi }{3}\cos \frac{7\pi }{6}\\ 2\sin \frac{7\pi }{3}\cos \frac{7\pi }{6}=0.2534\end{array}$

Taking the right hand side,

  $\begin{array}{c}-\cos x=-\cos \frac{7\pi }{6}\\ =-0.998\end{array}$

So, option D is not the solution of given equation.

So, option B, C and D are not the solution of given equation.