Trigonometric Functions of Angles

Question

Simplify tan(t)sec(t)

Answer 1

To see what tangent and secant really are, change them to sines and cosines:

tan(t) is really just (sin(t))/(cos(t))

sec(t) is really just 1/(cos(t))

Therefore (tan(t))(sec(t)) is really just (sin(t))/(cos²(t)), which doesn't simplify all that much.

Suggestion: maybe you meant to say "cosecant" instead of "secant"?

csc(t) is really just 1/(sin(t))

Therefore (tan(t))(csc(t)) is really just (sin(t))/((sin(t))(cos(t))), which simplifies to 1/(cos(t)) which simplifies to sec(t).

Answer 2

tan(t)sec(t) = [sin(t) / cos(t)][1 / cos(t)] = sin(t) / (cos²(t))