sin25+sin210+sin215+......+sin2180

Asked by karthikeyainuguri2009 | 10th Apr, 2022, 03:01: PM

Expert Answer:

To find sin25 + sin210 + sin215 + ... + sin290 + sin295 + sin2100 + ... +sin2180
sin squared 5 plus sin squared 10 plus... plus sin squared 85 plus sin squared 90 plus sin squared left parenthesis 180 minus 85 right parenthesis plus sin squared left parenthesis 180 minus 80 right parenthesis plus... plus sin squared left parenthesis 180 minus 5 right parenthesis plus sin squared 180
equals sin squared 5 plus sin squared 10 plus... plus sin squared 85 plus sin squared 90 plus cos squared 85 plus cos squared 100 plus... plus cos squared 5 plus sin squared 180
equals open parentheses sin squared 5 plus cos squared 5 close parentheses plus open parentheses sin squared 10 plus cos squared 10 close parentheses... plus open parentheses sin squared 85 plus cos squared 85 close parentheses plus sin squared 90 plus sin squared 180
equals stack stack 1 plus 1 plus... plus 1 with underbrace below with 85 space times below plus 1 plus 1
equals 87

Answered by Renu Varma | 11th Apr, 2022, 10:50: AM