sinA/tanA - tanA/secA

secY cosY - cos^2Y

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(sinx)^2+(cosx)^2=1 is the fundamental identity. Divide through by (sinx)^2: 1+(ctnx)^2=1/(sinx)^2 so sinx(1+ctn^2x)=sinx/(sinx)^2=1/sinx=cscx.

ctn^2x/(1+ctn^2x): multiply top and bottom by tan^2x: 1/(tan^2x+1)=1/sec^2x=cos^2x.

sinA/tanA-tanA/secA: sinAcosA/sinA-sinA/1=cosA-sinA.


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