Question

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)

Answer 1

sec²(x)

Step-by-step explanation:

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)