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Find Σ (sinx/sin2xsin3x)+(sinx/sin3xsin4x)...........n terms

Find  Σ (sinx/sin2xsin3x)+(sinx/sin3xsin4x)...........n terms

Grade:11

1 Answers

Param
25 Points
5 years ago
 
if you see carefully the difference in angles is constant ie. 3x-2x, 4x-3x, …..
 
=\frac{sin(3x-2x)}{sin3xsin2x} + ..... +\frac{sin[(n+1)x-(n)x]}{sin(n+1)xsin(n)x}
 
=\frac{sin3xcos2x-sin2xcos3x}{sin3xsin2x} + ..... +\frac{sin(n+1)xcos(n)x-sin(n)xcos(n+1)x}{sin(n+1)xsin(n)x}
 
=cot2x-cot3x + cot3x-cot4x + ..... +cot(n)x-cot(n+1)x
 
from symmetry of the equation...
 
=cot2x-cot(n+1)x...A.N.S
 
This is how all the symmetry questions can be attempted... All the best...

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