Simplify using trig identities:

Useful identities:     ======answer:     ======    use cofunction identity to convert into sine    use odd tangent identity to move the negative out from tangent:     use the tangent identity      we have two fractions with unlike denominators. let us get them to have the same denominator (this usually leads to more simplification).multiply numerator and denominator of  by  .    multiply numerator and denominator of  by      same denominators mean we can combine the fractions:     distribute in the numerator:     addition order does not matter; rearrange so that cos²  θ  is added on to sin² θ    use pythagorean identity to replace that boxed part with 1.    the  cancel out and we are left with    which is, by definition, secant because secant is the reciprocal of cosine.