Question

Use the fundamental identities to simplify the expression.

cos(pi/2 - x) * sec(x)

Answer 1

To simplify the expression, we can use the fundamental identities for cosine and secant.

First, let's rewrite the expression using the cosine fundamental identity:

cos(pi/2 - x) = sin(x)

The expression now becomes:

sin(x) * sec(x)

Next, let's use the fundamental identity for secant:

sec(x) = 1/cos(x)

Substituting this into the expression:

sin(x) * (1/cos(x))

Now we can simplify further by multiplying the two terms:

sin(x) / cos(x)

This expression can be simplified using the fundamental identity for tangent:

sin(x) / cos(x) = tan(x)

Therefore, the simplified expression is:

tan(x)