Question

Cos²3x-sin²3x+cos6x*cos3x​

Answer 1

$\cos^23x-\sin^23x+\cos6x\cos3x=\cos6x+\cos 6x\cos 3x=\cos 6x(1+\cos 3x)$

Answer 2

To simplify the expression cos²(3x) - sin²(3x) + cos(6x) * cos(3x), you can use some trigonometric identities.

1. Recall the trigonometric identity for cos(2θ): cos(2θ) = cos²(θ) - sin²(θ)

2. We can use this identity for θ = 3x to simplify cos²(3x) - sin²(3x): cos(2(3x)) = cos(6x) = cos²(3x) - sin²(3x)

3. Now, we can rewrite the expression: cos²(3x) - sin²(3x) + cos(6x) * cos(3x)

4. Replace cos(6x) with the expression from step 2: cos(2(3x)) - sin²(3x) + cos(6x) * cos(3x)

5. Now, substitute the identity cos(2θ) for the first term: cos(2(3x)) = cos(6x)

So, the simplified expression is: cos(6x) - sin²(3x) + cos(6x) * cos(3x)

You can leave it in this form, or you can simplify it further if needed.