The period of the function fx-sin 8x cos x -sin 6x cos 3x cos 2x cos x -sin 3x sin 4x is

The correct option is A π 2 f(x)=sin 8x cos x sin 6x cos 3x #160;cos 2x cos x sin 3x sin 4x #160; =( sin 9x +sin 7x #160;) ( sin ...

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Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

The period of...

Question

The period of the function
$f (x) = \frac{sin 8 x cos x - sin 6 x cos 3 x}{cos 2 x cos x - sin 3 x sin 4 x}$ is

π

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2 π

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\frac{π}{2}

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N o n e o f t h e s e

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Solution

The correct option is A $\frac{π}{2}$
$f (x) = \frac{sin 8 x cos x - sin 6 x cos 3 x}{cos 2 x cos x - sin 3 x sin 4 x}$
$= \frac{(sin 9 x + sin 7 x) - (sin 9 x + sin 3 x)}{(cos 3 x + cos x) + (cos 7 x - cos x)} = tan 2 x$
$∴$ Period of $f (x) = \frac{π}{2}$

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The period of the functionf(x)=sin8xcosx−sin6xcos3xcos2xcosx−sin3xsin4x is

The correct option is A π2f(x)=sin8xcosx−sin6xcos3xcos2xcosx−sin3xsin4x=(sin9x+sin7x)−(sin9x+sin3x)(cos3x+cosx)+(cos7x−cosx)=tan2x∴ Period of f(x)=π2

The period of the function
$f (x) = \frac{sin 8 x cos x - sin 6 x cos 3 x}{cos 2 x cos x - sin 3 x sin 4 x}$ is

The correct option is A $\frac{π}{2}$
$f (x) = \frac{sin 8 x cos x - sin 6 x cos 3 x}{cos 2 x cos x - sin 3 x sin 4 x}$
$= \frac{(sin 9 x + sin 7 x) - (sin 9 x + sin 3 x)}{(cos 3 x + cos x) + (cos 7 x - cos x)} = tan 2 x$
$∴$ Period of $f (x) = \frac{π}{2}$