Establish the identitytan u sec u cos u1 sin u Write the

Establish the identity.tan u - sec u = - cos u/1 + sin u Write the left side in terms of sine and cosine. tan u - sec u = sin u/cos u - 1/cos u Simplify by writing the expression from the previous step over a common denominator. -1 + sinu/cos u Rewrite the expression from the previous step by multiplying the numerator and denominator by sin u + 1. cos u(sin u + 1) (Simplify your answer.) Write the numerator of the expression from the previous step in terms of cosine. cos u(sin u + 1) cos u The fraction from the previous step then simplifies to -cos u/1 + sin u using what? Quotient Identity Cancellation Property

Solution

tanu -secu

=(sinu/cosu)-(1/cosu)

=(sinu -1)/(cosu)

multiply numerator and denominator by sinu +1

=[(sinu -1)(sinu +1)]/[(cosu)(sinu +1)]

=[(sin²u -1²)]/[(cosu)(sinu +1)]

=[(sin²u -1)]/[(cosu)(sinu +1)]

=(-cos²u)/[(cosu)(sinu +1)]

=(-cosu cosu)/[(cosu)(sinu +1)]

cancel cosu in numerator and denominator

= -cosu/(sinu +1)

=-cosu/(1+sinu)

cancellation property