Verify that each equation is an identity.
(tan² α + 1)/ sec α = sec α

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

Concept Check Suppose that sec θ = (x+4)/x.

Find an expression in x for tan θ.

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.

Perform each transformation. See Example 2.

Write cot x in terms of csc x.

Verify that each equation is an identity.

sin² β (1 + cot² β) = 1

Verify that each equation is an identity.

2 cos³ x - cos x = (cos² x - sin² x)/sec x

Perform each transformation. See Example 2.

Write sec x in terms of sin x.