The number of values of x for which sin 2x + | vedclass

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(A) Given the equation $\sin 2x + \cos 4x = 2$.We know that the maximum value of $\sin 	heta$ is $1$ and the maximum value of $\cos 	heta$ is $1$.Fo

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$0$

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(A) Given the equation $\sin 2x + \cos 4x = 2$.We know that the maximum value of $\sin 	heta$ is $1$ and the maximum value of $\cos 	heta$ is $1$.For the sum to be $2$,both terms must simultaneously take their maximum values:$\sin 2x = 1$ and $\cos 4x = 1$.Using the identity $\cos 4x = 1 - 2\sin^2 2x$,we substitute $\sin 2x = 1$ into the equation:$\cos 4x = 1 - 2(1)^2 = 1 - 2 = -1$.However,we require $\cos 4x = 1$.Since $-1 
eq 1$,there are no values of $x$ that satisfy the equation.Thus,the number of values of $x$ is $0$.

The number of values of $x$ for which $\sin 2x + \cos 4x = 2$ is

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