sinx+sin 2 x=1 what is the value of sin 10 x+sin 8 x+3(sin 6 x+sin 4 x)+sin 2 x-1

Question

Rinkoo Gupta · Answer

sin 8 x (sin 2 x +1) +3sin 4 x(sin 2 x+1) +sin 2 x-1 sin 8 x(1-sinx+1)+3sin 4 x(1-sinx+1)+1-sinx-1 sin 8 x(2-sinx)+3sin 4 x(2-sinx)-sinx (2-sinx)(sin 8 x+3sin 4 x) -sinx (2-sinx)sin 4 x(sin 4 x+3) -sinx (2-sinx)sin 4 x{(1-sinx) 2 +3} -sinx sin 4 x(2-sinx){1+sin 2 x-2sinx+3} -sinx sin 4 x(2-sinx)(1+1-sinx-2sinx+3) -sinx sin 4 x(2-sinx)((5-3sinx) -sinx sin 4 x(10-6sinx-5sinx+3sin 2 x) -sinx sin 4 x[10-11sinx+3(1-sinx)]-sinx sin 4 x[13-14sinx]-sinx (1-sinx) 2 (13-14sinx) -sinx (1+sin 2 x-2sinx)(13-14sinx)-sinx (1+1-sinx-2sinx)(13-14sinx)-sinx (2-3sinx)(13-14sinx)-sinx 26-28sinx-39sinx+42sin 2 x -sinx 26-67six+42(1-sinx) -sinx 26-68sinx+42-42sinx 68-110sinx sin 2 x+sinx-1=0 solving by shridharacharya method we get sinx=(sqrt5-1)/2 so the value ofsin 10 x+sin 8 x+3(sin 6 x+sin 4 x)+sin 2 x-1 =68-110sinx =68-110(sqrt5-1)/2 =68-55(sqrt5-1) =68-55sqrt5+55 =123-55sqrt5 Ans. Thanks & Regards Rinkoo Gupta AskIITians Faculty

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sinx+sin 2 x=1 what is the value of sin 10 x+sin 8 x+3(sin 6 x+sin 4 x)+sin 2 x-1

sinx+sin²x=1
what is the value of sin¹⁰ x+sin⁸ x+3(sin⁶ x+sin⁴ x)+sin² x-1

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sinx+sin 2 x=1 what is the value of sin 10 x+sin 8 x+3(sin 6 x+sin 4 x)+sin 2 x-1

sinx+sin2x=1what is the value of sin10 x+sin8 x+3(sin6 x+sin4 x)+sin2 x-1

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sinx+sin²x=1
what is the value of sin¹⁰ x+sin⁸ x+3(sin⁶ x+sin⁴ x)+sin² x-1