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If $\sin A+\sin B+\sin C=3$ then what is $\cos A+\cos B+\cos$
C equal to?
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C equal to?
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Verified Answer
The correct answer is:
$\underline{0}$
Let \sin A+\sin B+& \sin C=3 \end{aligned}$
$\Rightarrow \sin A=\sin B=\sin C=1 \quad(\because$ max value of sin is 1$)$
$\therefore \cos A=\sqrt{1-\sin ^{2} A}=\sqrt{1-1}=0$
Similarly, $\cos B=0=\cos C$
Hence, $\cos A+\cos B+\cos C=0+0+0=0$
$\Rightarrow \sin A=\sin B=\sin C=1 \quad(\because$ max value of sin is 1$)$
$\therefore \cos A=\sqrt{1-\sin ^{2} A}=\sqrt{1-1}=0$
Similarly, $\cos B=0=\cos C$
Hence, $\cos A+\cos B+\cos C=0+0+0=0$
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