Question

Can u help me solve this ​

Answer 1

Step-by-step explanation:

Rewrite the left side in terms of sine and cosine, then rearrange.

`(1+\tan^2{A})+(1+\frac{1}{\tan^2{A}})=\frac{1}{\sin^2{A}-\sin^4{A}}\\\\(1+\frac{\sin^2{A}}{\cos^2{A}})+(1+\frac{\cos^2{A}}{\sin^2{A}})=\\\\\frac{\sin^2{A}+\cos^2{A}}{\cos^2{A}}+\frac{\sin^2{A}+\cos^2{A}}{\sin^2{A}}=\\\\\frac{1}{\cos^2{A}}+\frac{1}{\sin^2{A}}=\\\\\frac{\sin^2{A}+\cos^2{A}}{(\sin^2{A})(\cos^2{A})}=\\\\\frac{1}{(\sin^2{A})(1-\sin^2{A})}=\frac{1}{\sin^2{A}-\sin^4{A}} \qquad\text{Q.E.D.}`