Introduction of Trigonometry — Maths STD 10 — Question
CBSE BoardEnglish MediumSTD 10MathsIntroduction of Trigonometry1 Mark
MCQ
If $\cos\text{A}+\cos^2\text{A}=1$ then $\big(\sin^2\text{A}+\sin^4\text{A}\big)=?$
A
$\frac{1}2{}$
B
$2$
✓
$1$
D
$4$
✓
Answer
Correct option: C.
$1$
$\cos\text{A}+\cos^2\text{A}=1$
$\Rightarrow\cos\text{A}=\sin^2\text{A}\dots(\text{i})$
Squaring both sides of $(i),$ we get:
$\cos^2\text{A}=\sin^4\text{A}\dots(\text{ii})$
Adding $(i)$ and $(ii),$ we get:
$\sin^2\text{A}=\sin^4\text{A}=\cos\text{A}+\cos^2\text{A}$
$\Rightarrow\sin^2\text{A}+\sin^4\text{A}$
$=1\ [\because\cos\text{A}+\cos^2\text{A}=1]$
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