Write the trigonometric expression as an algebraic expression. sin(arctan 6x − arccos x)

Answer 1

Let θ=arctan 6x, then sin θ=6x/sqrt(1+36x²) and cos θ=1/sqrt(1+36x²).

Let Φ=arccos x, then sin Φ=sqrt(1-x²) and cos Φ=x

Now use these values to compute sin θ cos Φ - cos θ sin Φ.

This expression will be messy (at best) and may be able to be collected and simplified.