Flag Trigonometry> sinx+sin 2 x=1 what is the value of sin 1...
question mark

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

kipan halder , 10 Years ago
Grade 11
anser 1 Answers
Rinkoo Gupta

Last Activity: 10 Years ago

sin8x (sin2x +1) +3sin4x(sin2x+1) +sin2x-1
sin8x(1-sinx+1)+3sin4x(1-sinx+1)+1-sinx-1
sin8x(2-sinx)+3sin4x(2-sinx)-sinx
(2-sinx)(sin8x+3sin4x) -sinx
(2-sinx)sin4x(sin4x+3) -sinx
(2-sinx)sin4x{(1-sinx)2+3} -sinx
sin4x(2-sinx){1+sin2x-2sinx+3} -sinx
sin4x(2-sinx)(1+1-sinx-2sinx+3) -sinx
sin4x(2-sinx)((5-3sinx) -sinx
sin4x(10-6sinx-5sinx+3sin2x) -sinx
sin4x[10-11sinx+3(1-sinx)]-sinx
sin4x[13-14sinx]-sinx
(1-sinx)2(13-14sinx) -sinx
(1+sin2x-2sinx)(13-14sinx)-sinx
(1+1-sinx-2sinx)(13-14sinx)-sinx
(2-3sinx)(13-14sinx)-sinx
26-28sinx-39sinx+42sin2x -sinx
26-67six+42(1-sinx) -sinx
26-68sinx+42-42sinx
68-110sinx
sin2x+sinx-1=0
solving by shridharacharya method we get sinx=(sqrt5-1)/2
so the value ofsin10x+sin8x+3(sin6x+sin4x)+sin2x-1
=68-110sinx
=68-110(sqrt5-1)/2
=68-55(sqrt5-1)
=68-55sqrt5+55
=123-55sqrt5 Ans.
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments