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
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