What is the simplified value of \(\frac{\sec^2 x-1}{\tan^2 x}\)?
Answer and explanation
Correct answer: \(1\)
Using the identity \(\sec^2 x=1+\tan^2 x\), we get \(\sec^2 x-1=\tan^2 x\). Therefore, \(\frac{\sec^2 x-1}{\tan^2 x}=\frac{\tan^2 x}{\tan^2 x}=1\), wherever the given expression is defined. Option \(0\) is incorrect because the numerator and denominator are equal; when they are zero, the fraction is undefined rather than zero. Exam tip: Replace \(\sec^2 x-1\) directly with \(\tan^2 x\).
Frequently asked questions
What is the correct answer to this question?
\(1\)
Why is this the correct answer?
Using the identity \(\sec^2 x=1+\tan^2 x\), we get \(\sec^2 x-1=\tan^2 x\). Therefore, \(\frac{\sec^2 x-1}{\tan^2 x}=\frac{\tan^2 x}{\tan^2 x}=1\), wherever the given expression is defined. Option \(0\) is incorrect because the numerator and denominator are equal; when they are zero, the fraction is undefined rather than zero. Exam tip: Replace \(\sec^2 x-1\) directly with \(\tan^2 x\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
