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Question: The expression \(\Rightarrow\) \(\sin 4\theta(2\cos 3\theta - 1) = 0 \Rightarrow \sin 4\theta = 0,\ ...

The expression \Rightarrow sin4θ(2cos3θ1)=0sin4θ=0, cos3θ=12\sin 4\theta(2\cos 3\theta - 1) = 0 \Rightarrow \sin 4\theta = 0,\ \cos 3\theta = \frac{1}{2} has the positive values for x, given by.

A

4θ=04\theta = 0

B

\Rightarrow

C

For all 4θ=π4\theta = \pi

D

\Rightarrow

Answer

For all 4θ=π4\theta = \pi

Explanation

Solution

The expression is

\Rightarrow

= 2cos2θ3cosθ3=02\cos^{2}\theta - \sqrt{3}\cos\theta - 3 = 0

Obviously, \Rightarrow. Hence it is positive for all value of x.