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A day full of math games & activities. Find one near you.
Prove cos 3x = 4cos3x−3cosx
We can prove cos 3x = 4cos3x−3cosx using trigonometric identity
Answer: cos 3x = 4cos3x−3cosx
Let us see how we can prove this.
Explanation:
cos 3x can be written as cos3x = cos(2x+x)—–(i)
As we know the trigonometric identity: cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
Applying the trigonometric identity to equation (i) and we get,
cos 3x = cos2x cosx − sin2x sinx
= (−1+2cos2x)cosx − 2cosx sinx sinx
= −cosx+2cos3x − 2sin2x cosx
= −cosx+2cos 3x − 2(1−cos2x)cosx
= −3cosx + 4cos3x
= 4cos3x − 3cosx
Hence, cos 3x = 4cos3x−3cosx
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