Question #b1c51

1 Answer
Jim G.
Jan 13, 2018

#-6#

Explanation:

#"using the "color(blue)"trigonometric identity"#

#•color(white)(x)sin^2theta+cos^2theta=1#

#rArrcostheta=+-sqrt(1-sin^2theta)#

#"since "theta" is acute then"#

#costheta=+sqrt(1-(20/29)^2)#

#color(white)(costheta)=sqrt(1-400/841)=sqrt(441/841)=21/29#

#rArr(3sintheta+4costheta)/(3sintheta-4costheta)#

#=(3xx20/29+4xx21/29)/(3xx20/29-4xx21/29)#

#=(60/29+84/29)/(60/29-84/29)#

#=144/29xx-29/24=-144/24=-6#

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