Question

sin²5°+sin²10°+sin²15°+...sin²90°

Answer 1

Answer:

sin²5° +sin²10° + sin²15° +.........sin²90°

= (sin²5° + sin²85° )+(sin²10°+sin²80°) +....+(sin²40° +sin²50° )+sin²45° +sin²90°

= [sin²5° +sin²(90°-5°)] +[sin²10°+sin²(90°-10°)]+....+[sin²40° +sin²(90°-40°)] +sin245° +sin²90°

= (sin²5° +cos²5° ) +(sin²10°+cos²10°)+....+(sin²40° +cos²40°)+sin²45°+sin²90°

=1+1+1+1+1+1+1+1+(1/√2)²+1

=9+1/2

= 9+1/2 =19/2 Answer ...