Number of values of x for which sin,, 2x + cos,, 4x = 2 is

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Trigonometrical Equations

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

A

$0$

B

$1$

C

$2$

D

infinite

Solution

$\sin 2 x+\cos 4 x=2$

$\Rightarrow \quad \sin 2 x=1, \cos 4 x=1$

$\Rightarrow \quad 1-2 \sin ^{2} 2 x=1$

$\Rightarrow \quad 1-2=1$ which is absurd

Hence there is no solution.

Standard 11

Mathematics

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