Question #990b4

1 Answer
Jim G.
Dec 11, 2017

#-2#

Explanation:

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

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

#rArr(1-(sintheta+costheta)(sintheta+costheta))/(sinthetacostheta)#

#"expand the factors on the numerator using FOIL"#

#=(1-sin^2theta-2costhetasintheta-cos^2theta)/(sinthetacostheta)#

#=(cancel(cos^2theta)-2costhetasinthetacancel(-cos^2theta))/(sinthetacostheta)#

#=(-2cancel(costheta)cancel(sintheta))/(cancel(sintheta)cancel(costheta)#

#=-2#

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