What is the very first step?

Geometry Level 3

The number of solutions of the equation 3 cos ⁡ 2 ( x ) sin ⁡ 2 ( x ) sin ⁡ 4 ( x ) cos ⁡ 2 ( x ) = 0 3\cos^2 (x) \sin^2 (x) \sin^4 (x) \cos^2 (x) = 0 in the interval [ 0 , 2 π ] [0,2\pi] is?


The answer is 4.

Mridul Jain by mridul jain , 21, India

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1 solution

Gary Popkin
Sep 19, 2015

The only way the monster product can be zero is for at least one of the factors to be zero. This happens at x x = 0, π \pi and again at x x = π \pi /2, 3 π \pi /2. The poster of the problem says the answer is four, but what about 2 π \pi ?

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