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  • Find the value of   <img alt="\sin55^{\circ}+\sin65^{\circ}+\sqrt{3}\cos{175^{\circ}}" src="http://entrancecorner.oncodecogs.com/gif.latex?%5Csin55%5E%7B%5Ccirc%7D&plus;%5Csin65%

Find the value of   \sin55^{\circ}+\sin65^{\circ}+\sqrt{3}\cos{175^{\circ}}

 

Option: 1

1


Option: 2

\frac{\sqrt{3}}{2}


Option: 3

0


Option: 4

\frac{1}{2}


Answers (1)

best_answer

Sum/Difference into Product-

\\1.\;\;\sin \alpha+\sin \beta=2 \sin \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)\\\\2.\;\;\sin \alpha-\sin \beta=2 \sin \left(\frac{\alpha-\beta}{2}\right) \cos \left(\frac{\alpha+\beta}{2}\right)\\\\3.\;\;\cos \alpha-\cos \beta=-2 \sin \left(\frac{\alpha+\beta}{2}\right) \sin \left(\frac{\alpha-\beta}{2}\right)\\\\4.\;\;\cos \alpha+\cos \beta=2 \cos \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)

Now,

\sin55^{\circ}+\sin65^{\circ}+\sqrt{3}\cos{175^{\circ}}\\\\=2\sin(\frac{55+65}{2})\cos(\frac{55-65}{2})+\sqrt{3}\cos{175^{\circ}}\\ =2\sin60^{\circ}\cos(-5^{\circ})+\sqrt{3}\cos{(180-5)^{\circ}}\\ =2\frac{\sqrt{3}}{2}\cos(-5^{\circ})+\sqrt{3}\cos{(180-5)^{\circ}}\\ =\sqrt{3}\cos(-5^{\circ})-\sqrt{3}\cos{(5)^{\circ}}\\ =0

Posted by

shivangi.shekhar

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