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