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Class 12 Mathematics Trigonometric Functions Trigonometric functions and their propertiesMediumLevel 71

What is the simplified value of \(\frac{1}{1+\sin x}+\frac{1}{1-\sin x}\)?

Answer and explanation

Correct answer: \(2\sec^2 x\)

Combining denominators gives \(\frac{2}{1-\sin^2 x}\). This is \(\frac{2}{\cos^2 x}=2\sec^2 x\).

Tags

rational-expressionsinesecant

Frequently asked questions

What is the correct answer to this question?

\(2\sec^2 x\)

Why is this the correct answer?

Combining denominators gives \(\frac{2}{1-\sin^2 x}\). This is \(\frac{2}{\cos^2 x}=2\sec^2 x\).

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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