Concept Check Suppose that sec θ = (x+4)/x.
Find an expression in x for tan θ.

For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.

sec x/csc x

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.

1/ tan² α + cot α tan α

For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.

cos² x

Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.

1 - 1/sec² x

Verify that each equation is an identity.

tan α/sec α = sin α

Perform each transformation. See Example 2.

Write cot x in terms of sin x.

Verify that each equation is an identity.

(tan² α + 1)/ sec α = sec α

Perform each transformation. See Example 2.

Write cot x in terms of csc x.