If sin 1 + sin 2 + sin 3 = 3 , then cos 1 + cos 2 + cos 3 =

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Solution

Q.
If $\sin θ_{1} + \sin θ_{2} + \sin θ_{3} = 3,$ then $\cos θ_{1} + \cos θ_{2} + \cos θ_{3} =$

Ans.
(0)

Since $\sin θ \in [- 1, 1]$

and   $\sin θ_{1} + \sin θ_{2} + \sin θ_{3} = 3$

$\Rightarrow$ $each \sin θ = 1$

$∴$    $each \cos θ = 0$

Hence,   $\cos θ_{1} + \cos θ_{2} + \cos θ_{3} = 0$

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