Prove that : `1-(sinAsin(90^(@)-A))/(cot(90^(@)-A))=sin^(2)A`

Prove that: sinA.sin(60^(@)+A).sin(60^(@)-A)=1/4sinA

Prove that (cos theta cos(90^(@)-theta))/(cot(90^(@)-theta))=cos^(2)theta

Prove that (cos(90^(@)-theta))/(1+sin(90^(@)-theta))+(1+sin(90^(@)-theta))/(cos(90^(@)-theta))=2cosec theta

Prove that: (tan(90^(@)-theta)sec(180^(@)-theta)sin(-theta))/(sin(180^(@)+theta)cot(360^(@)-theta)csc(90^(@)-theta))=1

Prove that: (sin(180^(@)+theta)cos(90^(@)+theta)tan(270^(@)-theta)cot(360^(@)-theta))/(sin(360^(@)-theta)cos(360^(@)+theta)cos ec(-theta)sin(270^(@)+theta))=1

Prove that : (i) sinthetacos(90^(@)-theta)+sin(90^(@)-theta)costheta=1 (ii) sectheta" cosec"(90^(@)-theta)-tanthetacot(90^(@)-theta)=1 (iii) (sintheta*sec(90^(@)-theta)cot(90^(@)-theta))/("cosec"(90^(@)-theta)*costheta*tantheta)-(tan(90^(@)-theta))/(cottheta)=0 (iv) (1+sin(90^(@)-theta))/(cos(90^(@)-0))+(cos(90^(@)-theta))/(1+sin(90^(@)-0))=2"cosec"theta

Prove that : (cot(90^(@)-theta))/(tantheta)+("cosec"(90^(@)-theta)sintheta)/(tan(90^(@)-theta))=sec^(2)theta

Prove that :(sin theta cos(90^(0)-theta)cos theta)/(sin(90^(0)-theta))+(cos theta sin(90^(0)-theta)sin theta)/(cos(90^(@)-theta))=1csc^(2)(90^(@)-theta)-tan^(2)theta=cos^(2)(90^(@)-theta)+cos^(2)theta

Prove the following: (tan(90^(@)-A)cot A)/(cos ec^(2)A)-cos^(2)A=0

Prove the following: (tan(90^(0)-A)cot A)/(cos ec^(2)A)-cos^(2)A=0