MCQ
If $\sin A +\sin ^2 A=1$, then $\cos ^2 A+\cos ^4 A= ?$
- A$\frac{1}{2}$
- ✓$1$
- C$2$
- D$3$
✓
Answer
Correct option: B.
$1$
$\sin A+\sin ^2 A=1$
$\Rightarrow \sin A=1-\sin ^2 A=\cos ^2 A$
$\therefore \cos ^2 A+\cos ^4 A$
$=\sin A+\sin ^2 A$
$=1$
$\Rightarrow \sin A=1-\sin ^2 A=\cos ^2 A$
$\therefore \cos ^2 A+\cos ^4 A$
$=\sin A+\sin ^2 A$
$=1$
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