What is the simplified value of \(\frac{\cosec^2 x-1}{\cot^2 x}\)?
Answer and explanation
Correct answer: 1
Using the Pythagorean trigonometric identity \(\cosec^2 x=1+\cot^2 x\), we get \(\cosec^2 x-1=\cot^2 x\). Therefore, \(\frac{\cosec^2 x-1}{\cot^2 x}=\frac{\cot^2 x}{\cot^2 x}=1\), wherever the expression is defined. \(\cot^2 x\) is not the final answer because it is only the simplified numerator. Exam tip: remember \(\cosec^2 x=1+\cot^2 x\) alongside \(\sec^2 x=1+\tan^2 x\).
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
Using the Pythagorean trigonometric identity \(\cosec^2 x=1+\cot^2 x\), we get \(\cosec^2 x-1=\cot^2 x\). Therefore, \(\frac{\cosec^2 x-1}{\cot^2 x}=\frac{\cot^2 x}{\cot^2 x}=1\), wherever the expression is defined. \(\cot^2 x\) is not the final answer because it is only the simplified numerator. Exam tip: remember \(\cosec^2 x=1+\cot^2 x\) alongside \(\sec^2 x=1+\tan^2 x\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
