What is the simplified value of (\cos^2 x(1+\tan^2 x))?
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Answer and explanation
Correct answer: \(1\)
Using the identity \(1+\tan^2 x=\sec^2 x\), the expression becomes \(\cos^2 x\sec^2 x\). Since \(\sec^2 x=1/\cos^2 x\), its value is \(1\). \(\sec^2 x\) is only the value of the bracketed part, not of the complete expression. Exam tip: When you see \(1+\tan^2 x\), replace it with \(\sec^2 x\).
Frequently asked questions
What is the correct answer to this question?
\(1\)
Why is this the correct answer?
Using the identity \(1+\tan^2 x=\sec^2 x\), the expression becomes \(\cos^2 x\sec^2 x\). Since \(\sec^2 x=1/\cos^2 x\), its value is \(1\). \(\sec^2 x\) is only the value of the bracketed part, not of the complete expression. Exam tip: When you see \(1+\tan^2 x\), replace it with \(\sec^2 x\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
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