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The positive Integral value of n >3 and satisfying the equation : 1/sin (pi/n) =1/sin (2pi/n) + 1/sin (3pi /n ) , is

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Solution:    Put    fracpin=	heta .

               	herefore           frac1sin 2	heta =frac1sin 	heta -frac1sin 3	heta

              Rightarrow            frac12sin	heta cdot cos	heta =fracsin 3	heta -sin 	heta sin	heta cdot sin 3	heta

              Rightarrow            frac12cos 	heta =frac2cos 2	heta cdot sin 	heta sin 3	heta

              Rightarrow           sin 3	heta =sin 4	heta =sin (pi -4	heta )

              Rightarrow           7	heta =piRightarrow 	heta =fracpi7    

                	herefore         fracpin=fracpi7Rightarrow n=7.

Posted by

Deependra Verma

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