YagaYeetin
Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Ask your questions and receive precise answers from experienced professionals across different disciplines. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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

#SPJ2

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.