If _1+ _2+ _3=3, then write the valuue of _1+ _2+ _3. - Vidyadip

Question

If $\sin\theta_1+\sin\theta_2+\sin\theta_3=3,$ then write the valuue of $\cos\theta_1+\cos\theta_2+\cos\theta_3.$

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Answer

The maximum value for $\sin(\text{x})$ is 1 for all x.
So,
$\Rightarrow\sin\theta_1+\sin\theta_2+\sin\theta_3=3,$
$\Rightarrow\sin\theta_1=\sin\theta_2=\sin\theta_3=1$
$\Rightarrow\theta_1=\theta_2=\theta_3=90^\circ$
$\therefore\cos\theta_1=\cos\theta_2=\cos\theta_3=0$
$\therefore\cos\theta_1+\cos\theta_2+\cos\theta_3=0$

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