Question #27b72

1 Answer
Jim G.
Feb 11, 2018

#"see explanation"#

Explanation:

#"consider left side"#

#•color(white)(x)cottheta=1/tantheta"#

#rArrtantheta/(1-(1/tantheta))+(1/tantheta)/(1-tantheta)#

#"multiply numerators/denominators by "tantheta#

#=(tan^2theta)/(tantheta-1)+1/(tantheta-tan^2theta)#

#=(tan^2theta)/(tantheta-1)-1/(tantheta(tantheta-1)#

#=(tan^2theta)/(tantheta-1)xxtantheta/tantheta-1/(tantheta(tantheta-1)#

#=(tan^3theta-1)/(tantheta(tantheta-1))larrcolor(blue)"difference of cubes"#

#=((cancel(tantheta-1))(tan^2theta+tantheta+1))/(tanthetacancel((tantheta-1))#

#=tantheta+1+1/tantheta#

#=1+(sintheta/costheta+costheta/sintheta)#

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

#=1+1/(sinthetacostheta)#

#=1+secthetacsctheta=" right side"#

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