Sin3x formula in terms of cosx is expressed as follows: sin3x = (4cos^{2}x-1)√(1-cos^{2}x). Here we learn how to prove sin3x formula in terms of cosine of x.

## sin3x in Terms of cos x

In order to express sin3x formula in terms of cosx, we will use the following trigonometric formulae:

- sin(a+b) = sin a cos b +cos a sin b
- sin 2a=2sin a cos a
- cos 2a = 2cos
^{2}a -1

Using the above formulas, we obtain the formula of sin3x in terms of cosx as follows:

sin3x

= sin(2x+x)

= sin2x cos x +cos2x sin x by the above formula (1)

= (2sin x cos x) cos x +(2cos^{2}x- 1) sin x by the above formulas (2) and (3).

= 2cos^{2}x sinx + 2cos^{2}x sinx – sinx

= 4cos^{2}x sinx – sinx

= (4cos^{2}x -1) sinx

= (4cos^{2}x -1) $\sqrt{1-\cos^2 x}$

Therefore, the formula of sin 3x in terms of cosx is given by sin3x = (4cos^{2}x-1)√(1-cos^{2}x).

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## FAQs

**Q1: What is the sin3x formula in terms of cosx?**

**Answer:** The sin3x formula in terms of cosx is given by sin3x = (4cos^{2}x-1)√(1-cos^{2}x).