Write cos(arcsin3x +arccos x) as an algebraic expression of x that does not involve trigonometric functions.

Step-by-step explanation:

Since we have to analyze the cosine of an addition of angles, let's recall that cos of an addition is:

Let's also use those Greek letters and to represent the inverse functions we are dealing with:

and therefore,

and therefore

Now use these identities to re-write the equation for the cos of an addition given above:

Now recall that the sine of an angle can be written in terms of the cos of the same angle via the Pythagorean identity:

In our case, and with our particular values, this gives:

Similarly we can write the cos of an angle in terms of the sine of the same angle:

In ours case, using our values, this gives:

So replacing these in the cos of an addition of angles formula, we obtain that the given expression equals:

answer:

step-by-step explanation: