sinx+sin2x=1what is the value of sin10 x+sin8 x+3(sin6 x+sin4 x)+sin2 x-1
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
Trigonometry> sinx+sin 2 x=1 what is the value of sin 1...
1 AnswersRinkoo 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
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available
Last Activity: 2 Years ago
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
0 Answer Available
Last Activity: 3 Years ago
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
0 Answer Available
Last Activity: 3 Years ago
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
trigonometry
0 Answer Available
Last Activity: 3 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
0 Answer Available
Last Activity: 3 Years ago