prove that : sin4180/16 + sin4 3x180/16 + sin4 5x180/16 + sin4 7x180/16 = 3/2 HERE x= multiplication sign , 180 = pie ------------------- Ankit Agrawal

put sin47x180/16 as sin4(8x180/16- 180/16) = cos4 180/16... Similarly,sin45x180/16 = cos43x180/16..the lhs can be rearranged to (sin4180/16 + cos4180/16) + (sin43x180/16 + cos43x180/16) = 1-2 (sin2180/16)(cos2180/16) + 1- 2 (sin23x180/16)(cos23x180/16) = 2- [sin2(2x180/16)]/2 - [sin2(6x180/16)]/2... but sin2(6x180/16) = cos2(2x180/16) =>2-[sin2(2x180/16) + cos2(2x180/160]/2 = 2-1/2 = 3/2 = rhs

help@askiitians.com

+91-735-322-1155

BACK

Trigonometry> Compound angles...

prove that :

sin⁴180/16 + sin⁴ 3x180/16 + sin⁴5x180/16 + sin⁴7x180/16 = 3/2

HERE x= multiplication sign , 180 = pie

------------------- Ankit Agrawal

ankit agrawal , 13 Years ago

Grade 11

1 Answers

Nikhil Cherukupalli

put sin⁴7x180/16 as sin⁴(8x180/16- 180/16) = cos⁴ 180/16... Similarly,sin⁴5x180/16 = cos⁴3x180/16..

the lhs can be rearranged to (sin⁴180/16 + cos⁴180/16) + (sin⁴3x180/16 + cos⁴3x180/16)

= 1-2 (sin²180/16)(cos²180/16) + 1- 2 (sin²3x180/16)(cos²3x180/16)

= 2- [sin²(2x180/16)]/2 - [sin²(6x180/16)]/2... but sin²(6x180/16) = cos²(2x180/16)

=>2-[sin²(2x180/16) + cos²(2x180/160]/2 = 2-1/2 = 3/2 = rhs

Last Activity: 13 Years ago