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The positive integer value of n>3 satisfying the equation 1/sinpi/n =1/sin 2pi/n +1/sin3pi/n is?

The positive integer value of n>3 satisfying the equation 1/sinpi/n =1/sin 2pi/n +1/sin3pi/n is? 

Grade:11

2 Answers

Ravi
askIITians Faculty 69 Points
9 years ago
let pi/n is equal to x.
1/sinx= 1/sin 2x+ 1/sin 3x
bring the odd terms of 3x and x on the same side. Solve using C and D formula to get the product of 2 trigonometric ratios, one of which will cancel out leaving behind a linear equation with 2 trigonomtric ratios equated to each other. Form a general solution of the equation obtained. Probably 2ndvalue of the iteration of general solution obtained will give the value of n.
harsh raj
24 Points
6 years ago
Why at askiit people just show the ways doing the answer ,comm`on it`s irritating ,ok u wanna make us think but give us hints little detailed or in easier language?

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