prove that sine square eighteen degree plus cosine square thirty six degree  is equal to three by four

Asked by hrushikesh.barik | 30th Oct, 2017, 08:27: PM

Expert Answer:

begin mathsize 16px style sin squared 18 degree space plus space cos squared 36 degree
equals sin squared 18 degree space plus open parentheses 1 space minus space 2 sin squared 18 degree close parentheses squared........ left parenthesis straight i right parenthesis
Considering space straight A space equals space 18 degree
sin 36 degree space equals space sin open parentheses 90 degree minus 54 degree close parentheses
sin 36 degree space equals cos 54 degree
sin 2 straight A equals cos 3 straight A
Solving space this space we space get space
sin squared 18 degree space equals space fraction numerator 3 space minus space square root of 5 over denominator 8 end fraction
Put space this space value space in space equation space left parenthesis straight i right parenthesis
and space solving space it space further space we space get space
sin squared 18 degree space plus space cos squared 36 degree space equals space 3 over 4 end style

Answered by Sneha shidid | 13th Dec, 2017, 04:48: PM