Question

Simplify \(1-\sin^{4}\theta\):

• A. \(\cos^{2}\theta\,(1+\sin^{2}\theta)\)
• B. \(\cos^{2}\theta\,(1-\sin^{2}\theta)\)
• C. \(\cos^{2}\theta\,(1-\cos^{2}\theta)\)
• D. \(\sin^{2}\theta\,(1+\sin^{2}\theta)\)

Hint:

Use difference of squares and \(1-\sin^2\theta=\cos^2\theta\).

Answer 1

The Correct Option is A

\[ 1-\sin^{4}\theta=(1-\sin^{2}\theta)(1+\sin^{2}\theta)=\cos^{2}\theta(1+\sin^{2}\theta). \]