which of the following expressions is equivalent to cos3x/sinxcos x

Question

A. cscxcos2s-secsin2x
b. secxcos2x-cscxsin2x
c. secxcosx-cscxsinx
D. cscxcosx-secxsinx

Answer 1

The expression cos3x/sinxcosx can be simplified by using the trigonometric identity cos(3x) = 4cos^3(x) - 3cos(x).

So, cos3x = 4cos^3(x) - 3cos(x)

Dividing by sin(x)cos(x), we get:

(cos3x)/(sin(x)cos(x)) = (4cos^3(x) - 3cos(x))/(sin(x)cos(x))
= (4cos^2(x) - 3)(cos(x)/sin(x))
= 4cos^2(x)/sin(x) - 3cos(x)/sin(x)
= 4cot(x)cos(x) - 3csc(x)

Therefore, the expression is equivalent to:

4cot(x)cos(x) - 3csc(x)

So the correct answer is:

A. cscxcos2s-secsin2x