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Prove 1/(secx-tanx)-1/(cosx)=1/(cosx)-1/...

Prove `1/(secx-tanx)-1/(cosx)=1/(cosx)-1/(secx+tanx)`

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The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitrary constant K)dot -1/((secx+tanx)^((11)/2)){1/(11)-1/7(secx+tanx)^2}+K 1/((secx+tanx)^(1/(11))){1/(11)-1/7(secx+tanx)^2}+K -1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K 1/((secx+tanx)^((11)/2)){1/(11)+1/7(secx+tanx)^2}+K

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