What is the simplified value of (\sin^4 x-\cos^4 x)?
Answer and explanation
Correct answer: \(\sin^2 x-\cos^2 x\)
Using the difference of squares, \(\sin^4 x-\cos^4 x=(\sin^2 x-\cos^2 x)(\sin^2 x+\cos^2 x)\). Since \(\sin^2 x+\cos^2 x=1\), the simplified value is \(\sin^2 x-\cos^2 x\). Option B is its negative, so it is not correct. Exam tip: after applying \(a^2-b^2=(a-b)(a+b)\), use the fundamental trigonometric identity.
Frequently asked questions
What is the correct answer to this question?
\(\sin^2 x-\cos^2 x\)
Why is this the correct answer?
Using the difference of squares, \(\sin^4 x-\cos^4 x=(\sin^2 x-\cos^2 x)(\sin^2 x+\cos^2 x)\). Since \(\sin^2 x+\cos^2 x=1\), the simplified value is \(\sin^2 x-\cos^2 x\). Option B is its negative, so it is not correct. Exam tip: after applying \(a^2-b^2=(a-b)(a+b)\), use the fundamental trigonometric identity.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
