Solve cosA-sinA+1/cosA+sinA-1=cscA+cotAsqrt{1+11delta}

$$\frac { \cos A - \sin A + 1 } { \cos A + \sin A - 1 } = \csc A + \cot A \sqrt { 1 + 11 \delta }$$

Solve for δ

$$\left\{\begin{matrix}\delta =0\text{, }&\nexists n_{2}\in \mathrm{Z}\text{ : }A=\pi n_{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }A=2\pi n_{1}+\frac{\pi }{2}\\\delta \geq -\frac{1}{11}\text{, }&\exists n_{3}\in \mathrm{Z}\text{ : }A=2\pi n_{3}+\frac{3\pi }{2}\end{matrix}\right.$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\csc(A)+\cot(A)\sqrt{1+11\delta }=\frac{\cos(A)-\sin(A)+1}{\cos(A)+\sin(A)-1}$$

Subtract \csc(A) from both sides.

$$\cot(A)\sqrt{1+11\delta }=\frac{\cos(A)-\sin(A)+1}{\cos(A)+\sin(A)-1}-\csc(A)$$

Divide both sides by \cot(A).

$$\frac{\cot(A)\sqrt{11\delta +1}}{\cot(A)}=\frac{\cot(A)}{\cot(A)}$$

Dividing by \cot(A) undoes the multiplication by \cot(A).

$$\sqrt{11\delta +1}=\frac{\cot(A)}{\cot(A)}$$

Divide \cot(A) by \cot(A).

$$\sqrt{11\delta +1}=1$$

Square both sides of the equation.

$$11\delta +1=1$$

Subtract 1 from both sides of the equation.

$$11\delta +1-1=1-1$$

Subtracting 1 from itself leaves 0.

$$11\delta =1-1$$

Subtract 1 from 1.

$$11\delta =0$$

Divide both sides by 11.

$$\frac{11\delta }{11}=\frac{0}{11}$$

Dividing by 11 undoes the multiplication by 11.

$$\delta =\frac{0}{11}$$

Divide 0 by 11.

$$\delta =0$$

Solve for A

$$\left\{\begin{matrix}A=2\pi n_{2}+\frac{3\pi }{2}\text{, }n_{2}\in \mathrm{Z}\text{, }&\delta \geq -\frac{1}{11}\\A\notin 2\pi n_{1}+\frac{\pi }{2},\pi n_{1}\text{, }\forall n_{1}\in \mathrm{Z}\text{, }&\delta =0\end{matrix}\right.$$