What is \(\frac{1}{\sec x+\tan x}\) equal to?
Answer and explanation
Correct answer: \(\sec x-\tan x\)
Multiply the numerator and denominator by \(\sec x-\tan x\). The denominator becomes \((\sec x+\tan x)(\sec x-\tan x)=\sec^2x-\tan^2x=1\). Hence, \(\frac{1}{\sec x+\tan x}=\sec x-\tan x\). Option C is the negative of the required expression, so it is incorrect. Exam tip: use the identity \(\sec^2x-\tan^2x=1\) for reciprocal expressions of this form.
Frequently asked questions
What is the correct answer to this question?
\(\sec x-\tan x\)
Why is this the correct answer?
Multiply the numerator and denominator by \(\sec x-\tan x\). The denominator becomes \((\sec x+\tan x)(\sec x-\tan x)=\sec^2x-\tan^2x=1\). Hence, \(\frac{1}{\sec x+\tan x}=\sec x-\tan x\). Option C is the negative of the required expression, so it is incorrect. Exam tip: use the identity \(\sec^2x-\tan^2x=1\) for reciprocal expressions of this form.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
