MCQ
$\cos^4\text{A}-\sin^4\text{A}$ is equal to :
- A$2\cos^2\text{A}+1$
- ✓$2\cos^2\text{A}-1$
- C$2\sin^2\text{A}-1$
- D$2\sin^2\text{A}+1$
✓
Answer
Correct option: B.
$2\cos^2\text{A}-1$
$\cos^4\text{A}-\sin^4\text{A}=(\cos^2\text{A}+\sin^2\text{A})(\cos^2\text{A}-\sin^2\text{A})$
$=1(\cos^2\text{A}-\sin^2\text{A})=\cos^2\text{A}-(1-\cos^2\text{A})$
$=\cos^2\text{A}-1+\cos^2\text{A}$
$=2\cos^2\text{A}-1$
$=1(\cos^2\text{A}-\sin^2\text{A})=\cos^2\text{A}-(1-\cos^2\text{A})$
$=\cos^2\text{A}-1+\cos^2\text{A}$
$=2\cos^2\text{A}-1$
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