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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Mathematics
Chapter
Trigonometric Equations

BITSAT 2016 · Mathematics · Trigonometric Equations

If θ_ 1 + θ_ 2 + θ_ 3 =3, then θ_ 1 + θ_ 2 + θ^ 3 =

If sin⁡θ1+sin⁡θ2+sin⁡θ3=3,\sin \theta_{1}+\sin \theta_{2}+\sin \theta_{3}=3, then cos⁡θ1+cos⁡θ2+cos⁡θ3=\cos \theta_{1}+\cos \theta_{2}+\cos \theta^{3}=

Options

  1. A0
  2. B1
  3. C2
  4. D3

Correct answer

A. 0

Step-by-step solution

Since, sin⁡θ1+sin⁡θ2+sin⁡θ3=3\sin \theta_{1}+\sin \theta_{2}+\sin \theta_{3}=3∴sin⁡θ1=sin⁡θ2=sin⁡θ3=1⇒θ1=θ2=θ3=π2∴cos⁡θ1+cos⁡θ2+cos⁡θ3=0\begin{array}{ll}\therefore & \sin \theta_{1}=\sin \theta_{2}=\sin \theta_{3}=1 \Rightarrow \theta_{1}=\theta_{2}=\theta_{3}= \\ & \frac{\pi}{2} \\ \therefore & \cos \theta_{1}+\cos \theta_{2}+\cos \theta_{3}=0\end{array}$$
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