Show 3 cos &#x2061;<!-- ⁡ --> 2 x + 1 = 4 cos 2 </msup>

deformere692qr

deformere692qr

Answered question

2022-05-17

Show 3 cos 2 x + 1 = 4 cos 2 x 2 sin 2 x

Answer & Explanation

charringpq49u

charringpq49u

Beginner2022-05-18Added 23 answers

All you need to do is use the identity sin 2 x + cos 2 x = 1:
3 cos 2 x + 1 = 3 ( cos 2 x sin 2 x ) + 1 = 3 ( cos 2 x sin 2 x ) + sin 2 x + cos 2 x = 4 cos 2 x 2 sin 2 x
QED.
Alternatively, if you don't feel comfortable turning the 1 into sin 2 x + cos 2 x (and trust me, it's a perfectly valid thing to do), you can equivalently break out one of the existing sin 2 x and replace it with 1 cos 2 x , and as long as you get all the signs correct it amounts to the same thing.
Laila Andrews

Laila Andrews

Beginner2022-05-19Added 4 answers

I continue from where you left off.
3 cos 2 x 3 sin 2 x + 1 = 4 cos 2 x cos 2 x sin 2 x 2 sin 2 x + 1
= 4 cos 2 x 2 sin 2 x cos 2 x sin 2 x + 1
= 4 cos 2 x 2 sin 2 x .

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