Prove the trigonometric identities: `(1+cotA+t a n A)(sin A-cos A)=(s e c A)/(cos e c^2A)-(cos e cA)/(sec^2A)=sinAtanA-cotAcosA`

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 the trigonometric identities: (1)/( sec A+tan A)-(1)/(cos A)=(1)/(cos A)-(1)/(sec A-tan A)

Prove: (cos e c\ A)/(cos e c\ A-1)+(cos e c\ A)/(cos e c\ A+1)=2sec^2A

Prove: (1-cos^2A)cos e c^2A=1

Prove the following identities: (cotA+cos e cA-1)/(cotA-cos e cA+1)=(1+cosA)/(sinA)

Prove the following identity: (t a n A)/(1-cot A)+(cot A)/(1-t a n A)=(s e c A\ cos e c\ A+1)

Prove the following identities: 1/(cos e cA-cotA)-1/(sinA)=1/(sinA)-1/(cos e cA+cotA)

Prove the following identities: (tanA)/(1-cotA)+(cotA)/(1-tanA)=1+tanA+cotA=1+secAcos e cA

Prove the following identities: (tanA)/(1-cotA)+(cotA)/(1-tanA)=1+tanA+cotA=1+secAcos e cA

Prove the following identity: (1-sin AcosA)/(cos A(s e c A-cosec A))dot(sin^2A-cos^2A)/(sin^3 A+cos^3 A)=sin A