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Which expression does (cos 3x)(cos x) − (sin 3x)(sin x) simplify to?

cos 4x
sin 2x
cos 2x
sin 4x

Sagot :

Hrishii

Answer:

cos 4x

Step-by-step explanation:

[tex]( \cos 3x)( \cos x) − ( \sin 3x)( \sin x) \\ \\ = \cos \: (3x + x) \\ \\ = \cos \: 4x[/tex]

The result for the expression (cos 3x)(cos x) − (sin 3x)(sin x) is cos 4x.

Trigonometric Identities

What is trigonometric identities ?

Equations involving trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.

The addition/sum formula in trigonometry:

In terms of functions of A and B, angle addition formulae express trigonometric functions of sums of angles A[tex]\frac{+}{_}[/tex]B.

Sum formula or cos:

cos (A+B) = cosA.cosB + sinA.sinB

Application of sum formula of cos:

The give equation is as follows,

(cos 3x)(cos x) − (sin 3x)(sin x)

Applying the sum formula,

= (cos 3x)(cos x) − (sin 3x)(sin x)

= cos(3x + x)

= cos 4x

Therefore, the result of the given equation is cos 4x.

To know more about trigonometric ratios and their examples, here

https://brainly.com/question/24349828

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