Question

sin thita1+sin thita2+sin thita3=3, then cos thita1+cos thita2+cis thita3=?

Answer 1

Hey There!!!


We know that Minimum Value of $\sin\theta$ is -1, and the Maximum Value is +1.

Here, we are given that:
 
$\sin\theta_1+\sin\theta_2+\sin\theta_3=3$

Since maximum value of sine function is 1, all three terms must be equal to 1 for the sum to be equal to 3. 

That is, the above statment can be true if and only if: 

$\sin\theta_1 = 1 \, \, ,\sin\theta_2=1\,\,and\,\, \sin\theta_3=1 \\ \\ \\ \implies \theta_1=90^{\circ} \,\, , \theta_2=90^{\circ}\,\, , \theta_3=90^{\circ}$

Now, we can easily find the value of the second statement:
$\cos\theta_1+\cos\theta_2+\cos\theta_3 \\ \\ = \cos 90^{\circ}+\cos 90^{\circ}+\cos 90^{\circ} \\ \\ = 0+0+0 \\ \\ =0 \\ \\ \\ \implies \boxed{\cos\theta_1+\cos\theta_2+\cos\theta_3=0}$

Hence your answer is Option (d) -> 0


Hope it helps
Purva
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