62.2k views
1 vote
Can u help me solve this ​

Can u help me solve this ​-example-1

1 Answer

6 votes

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.}

User Cfchou
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories