Example 3 The value of sin2 5° +sin2 10°sin290° is+sin2 15° +... +

1.	Example 3 The value of sin2 5° +sin2 10°sin290° is+sin2 15° +... +sin2 85(a) 7(b) 822(c) 10(d) 922
Answer» from LHS 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 ...

Example 3 The value of sin2 5° +sin2 10°sin290° is+sin2 15° +... +sin2 85(a) 7(b) 822(c) 10(d) 922

Answer»

from LHS

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 ...