verify the identity cos2tsintcsctsintSolutioncos2tsint sin2t

verify the identity cos^2t/sint=csct-sint

cos²t/sint

sin²t+cos²t =1 is the identity =>cos²t =1 -sin²t

cos²t/sint

=(1 -sin²t)/sint

=1/sint -sin²t/sint

=1/sint -sint

=csct -sint

so cos²t/sint=csct -sint

verify the identity cos^2t/sint=csct-sintSolutioncos2t/sint sin2t+cos2t =1 is the identity =>cos2t =1 -sin2t cos2t/sint =(1 -sin2t)/sint =1/sint -sin2t/sint

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Dr Jack

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