Question

what is the formula of 1-cos3x​

Answer 1

Answer:

1 - cos 3 x = 3 sin 3 x

Step-by-step explanation:

• for further elaboration contact any mathematic students..

Answer 2

Formula of 1-cos3x is 1-4$cos^{3} x$-3cosx.

Given,

1-cos3x

To find,

Formula of 1-cos3x

Solution,

Cosine is a trigonometric function. Cosine is the ratio between the side next to an acute angle in a right angle and the hypotenuse.

We can write,

cos3x= cos(2x+x)

        = cos2xcosx - sin2xsinx

        = (1-2$sin^{2} x$)cosx - 2$sin^{2} x$cosx

        = cosx-$2sin^{2} xcosx$-$2sin^{2} xcosx$

        =cosx - $4sin^{2} cosx$

Using, $sin^{2} x+cos^{2} x$=1;

$sin^{2} x=1-cos^{2} x$

cos3x= cosx-4cosx+4$cos^{3} x$

         = 4$cos^{3} x$-3cosx

1-cos3x=1- 4$cos^{3}x$-3cosx.

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