Question

1-tan^2A/cot^2A-1=tan^2A

Answer 1

Proving L.H.S=R.H.S

Step-by-step explanation:

$\ Given \ value:\\\\\frac{1-\tan^2 A}{\cot^2 A-1 }= \tan^2 A\\\\\ Solution:\\\\ \frac{1-\tan^2 A}{\cot^2 A-1 }= \tan^2 A\\\\\ Solve \ L.H.S \ part: \\\\ \rightarrow \frac{1-\frac{\sin^2 A}{\cos^2 A}}{\frac{\cos^2 A}{\sin^2 A}-1 }\\\\\rightarrow \frac{\frac{\cos^2 A-\sin^2 A}{\cos^2 A}}{\frac{\cos^2 A-\sin^2 A}{\sin^2 A}}\\\\\rightarrow \frac{\cos^2 A-\sin^2 A}{\cos^2 A}}\times \frac{\sin^2 A}{\cos^2 A-\sin^2 A}}$

$\rightarrow \frac{\sin^2 A}{\cos^2 A} \\\\\rightarrow \tan^2 A$

L.H.S= R.H.S

Learn more:

• Proving: https://brainly.in/question/16419222