Sec 15 Multiply Simplify your answers completely for each of

(Sec 1.5) Multiply. Simplify your answers completely for each of the following.

A) (sin + 5)(sin + 6)

B) (4 tan )(4 + tan )

C) (sin 9)²

Solution

A) (sin + 5)(sin + 6)

=(sin )(sin + 6) +( 5)(sin + 6)

=sin²+6sin +5sin +30

=sin²+11sin+30

B) (4 tan )(4 + tan )

=(4 )(4 + tan ) + ( tan )(4 + tan )

=16 +4tan -4tan -tan²

=16-tan²

C) (sin 9)²

=(sin 9)(sin 9)

=(sin )(sin 9) +( 9)(sin 9)

=sin² -9sin -9sin +81

=sin² -18sin +81