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value of sin13+sin14+sin15+sin16.........sin99 angles are in degrees

value of sin13+sin14+sin15+sin16.........sin99
angles are in degrees

Grade:12th pass

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
6 years ago
Hello Student, Please find the solution

lets take n terms and than apply n->infinite

sin13 +sin15+sin17......+ sin[13+(n-1)2] + ….…
Apply summation of sine series formula if the angles are in A.P.


sin13 +sin15+sin17......+ sin[13+(n-1)2]
[=\frac{sin\frac{n*2}{2}}{sin*\frac{2}{2}}*sin[2*(13+(n-1)2)]]
[=\frac{sin(n)}{sin1}sin[22+4n]]

Now you can apply n->infinity to this question

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