Write the expression in terms of sine and cosine and simplify so that no quotients appear in the final expression. show work. tan² x (1 + cot² x)

sec²(x)

As required:

... = (sin²(x)/cos²(x))(1 +(cos²(x)/sin²(x))

... = (sin²(x)·(sin²(x)+cos²(x)) / (cos²(x)·sin²(x))

... = 1/cos²(x) = sec²(x)

Alternatively, multiply out the given expression, then use trig identities.

... = tan²(x) + (tan(x)·cot(x))² = tan²(x) +1 = sec²(x)

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.