Factor and simplify Type your answer in terms of sine andor

Factor and simplify. Type your answer in terms of sine and/or cosine. StartFraction 8 sine squared theta plus 6 sine theta plus 1 Over 2 sine squared theta plus 3 sine theta plus 1 EndFraction 8sin2 +6sin +1 2sin2 +3sin +1 StartFraction 8 sine squared theta plus 6 sine theta plus 1 Over 2 sine squared theta plus 3 sine theta plus 1 EndFraction 8sin2 +6sin +1 2sin2 +3sin +1

Solution

(8sin²+6sin+1)/_{(2sin²+3sin+1)}

=(8sin²+4sin+2sin+1)/_{(2sin²+2sin+sin+1)}

=(4sin(2sin+1)+1(2sin+1))/_{(2sin(sin+1)+1(sin+1))}

=((2sin+1)(4sin+1))/_{((sin+1)(2sin+1))}

=(4sin+1)/_(sin+1)