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

csc² t - 1

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

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.

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.

Verify that each equation is an identity.

sin² β (1 + cot² β) = 1