How do you prove that #(tan theta-cos theta)^2+ 4 sintheta= (tan theta+ cos theta)^2#?

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Answer 1 · 2018-04-05T13:44:16

See the proof below

#"Reminder"#

#tanthetaxxcostheta=sintheta/costhetaxx costheta=sintheta#

Therefore,

#LHS=(tantheta-costheta)^2+4sintheta#

#=tan^2theta+cos^2theta-2tanthetacostheta+4tantheta costheta#

#=tan^2theta+cos^2theta+2tanthetacostheta#

#=(tantheta+costheta)^2#

#=RHS#

#QED#