Question

EXAMPLE 3 The value of sin? 1° + sin ?5° + sin ? 9°
+ ... + sin ? 89° is​

Answer 1

sin²1+sin²89=1

sin²5+sin²85=1

sin²9+sin²81=1

sin²13+sin²77=1

sin²17+sin²73=1

sin²21+sin²69=1

sin²25+sin²65=1

sin²29+sin²61=1

sin²33+sin²57=1

sin²37+sin²53=1

sin²41+sin²49=1

sin²45=0.5

1+1+1+1+1+1+1+1+1+1+1+0.5=11.5

sin² 1°+sin² 5°+sin² 9°+…+sin² 89°=11.5