MCQ
The value of $\cos^4\text{x}+\sin^4\text{x}-6\cos^2\sin^2$ is:
- A$\cos2\text{x}$
- B$\sin2\text{x}$
- C$\cos4\text{x}$
- DNone of these
✓
Answer
- $\cos4\text{x}$
Solution:
$\cos^4\text{x}+\sin^4\text{x}-6\cos^2\text{x}\sin^2\text{x}=\cos^4\text{x}\\+\sin^4\text{x}-2\cos^2\text{x}\sin^2\text{x}-4\cos^2\text{x}\sin^2\text{x}$
$=(\cos^2\text{x}-\sin^2\text{x})^2-(2\sin\text{x}\cos\text{x})^2$
$=\cos^22\text{x}-\sin^22\text{x}$
$=\cos4\text{x}$
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