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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

NDA 2016 · Mathematics · Trigonometric Ratios & Identities

If θ_1+ θ_2+ θ_3+ θ_4=4 , then what is the value of θ_1+ θ_2+ θ_3+...

If sin⁡θ1+sin⁡θ2+sin⁡θ3+sin⁡θ4=4\sin \theta_1+\sin \theta_2+\sin \theta_3+\sin \theta_4=4, then what is the value of cos⁡θ1+cos⁡θ2+cos⁡θ3+cos⁡θ4=?\cos \theta_1+\cos \theta_2+\cos \theta_3+\cos \theta_4=?

Options

  1. A00
  2. B11
  3. C22
  4. D44

Correct answer

A. 00

Step-by-step solution

sin⁡θ1+sin⁡θ2+sin⁡θ3+sin⁡θ4=4\sin \theta_1+\sin \theta_2+\sin \theta_3+\sin \theta_4=4...(1) Since max. value of sin⁡θ=1WehavefourtermsinLHSof\sin \theta=1We have four terms in LHS ofeq. (1). \Rightarrow Every term should be=1=1⇒sin⁡θ1=sin⁡θ2=sin⁡θ3=sin⁡θ4=1⇒θ1=θ2=θ3=θ4=90∘\begin{aligned} & \Rightarrow \sin \theta_1=\sin \theta_2=\sin \theta_3=\sin \theta_4=1 \\ & \Rightarrow \theta_1=\theta_2=\theta_3=\theta_4=90^{{}^{\circ}} \end{aligned}$Now,Now,\cos \theta_1+\cos \theta_2+\cos \theta_3+\cos \theta_4=\left(\cos 90^{{}^{\circ}}\right) \times 4=0.$
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