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JEE Main 201226 MayOnline
Exam
JEE Main
Year
2012
Date
26 May
Mode
Online
Subject
Mathematics
Chapter
Trigonometric Ratios & Identities

JEE Main 2012 · 26 May · Online · Mathematics · Trigonometric Ratios & Identities

The value of 255^ + 195^ is

The value of cos⁡255∘+sin⁡195∘\cos 255^{\circ}+\sin 195^{\circ} is

Options

  1. A3−122\frac{\sqrt{3}-1}{2 \sqrt{2}}
  2. B3−12\frac{\sqrt{3}-1}{\sqrt{2}}
  3. C−3−12-\frac{\sqrt{3}-1}{\sqrt{2}}
  4. D3+12\frac{\sqrt{3}+1}{\sqrt{2}}

Correct answer

C. −3−12-\frac{\sqrt{3}-1}{\sqrt{2}}

Step-by-step solution

Consider cos⁡255∘+sin⁡195∘\cos 255^{{}^{\circ}}+\sin 195^{{}^{\circ}}=cos⁡(270∘−15∘)+sin⁡(180∘+15∘)=−sin⁡15∘−sin⁡15∘=−2sin⁡15∘=−2(3−122)=−(3−12)\begin{aligned}& =\cos \left(270^{{}^{\circ}}-15^{{}^{\circ}}\right)+\sin \left(180^{{}^{\circ}}+15^{{}^{\circ}}\right) \\ & =-\sin 15^{{}^{\circ}}-\sin 15^{{}^{\circ}} \\ & =-2 \sin 15^{{}^{\circ}}=-2\left(\frac{\sqrt{3}-1}{2 \sqrt{2}}\right)=-\left(\frac{\sqrt{3}-1}{\sqrt{2}}\right) \end{aligned}$$
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