[" 6.Prove that: "],[qquad ((1+cot A+tan A)(sin A-cos A))/(sec^(3)A-cosec^(3)A)=sin^(2)A*cos^(2)A]

Prove the following identities: (cos A)/(1-sin A)+(sin A)/(1-cos A)+1=(sin A cos A)/((1-sin A)(1-cos A))((1+cot A+tan A)(sin A-cos A)/(sec^(3)A-cos ec^(3)A)=sin^(2)A cos^(2)A

(sin A+cosec A)^(2)+(cos A+sec A)^(2)=7+tan^(2)A+cot^(2)A

Prove that: (cosec A-sin A)(sec A-cos A)=(1)/(tan A+cot A)

(1+tan A)/(sin A)+(1+cot A)/(cos A)=2(sec A+cosec A)

Prove that : (cosec A - sin A) (sec A - cos A) sec^(2) A = tan A

Prove that :(1+cot A+tan A)(sin A cos A)=sin A tan A cot A cos A

Prove that : (cos A cot A)/ (1 - sin A) = 1 + cosec A

Prove the trigonometric identities: (1+cot A+tan A)(sin A-cos A)=(sec A)/(cos ec^(2)A)-(cos ecA)/(sec^(2)A)=sin A tan A-cot A cos A

Prove that: ((1+cot theta+ tan theta)(sin theta-cos theta))/(sec^3 theta-cosec^3 theta)=sin^2 theta cos^2 theta

Prove that ( "cosec" A - sin A)(sec A- cos A)=(1)/((tan A+ cot A)).