the expression simplifies to sin2x + cos2x/sec x

Answer 1

To simplify the expression, first recall the Pythagorean identity:

sin^2(x) + cos^2(x) = 1

Now divide both sides of the identity by sec^2(x) to get:

(sin^2(x) + cos^2(x))/sec^2(x) = 1/sec^2(x)

Since sec(x) is equal to 1/cos(x), the expression simplifies to:

(sin^2(x) + cos^2(x))/sec^2(x) = 1/(1/cos^2(x)) = cos^2(x)