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The value of $sin^{2}1^{0} + sin^{2}2^{0} + sin^{2}3^{0}+.........+sin^{2}89^{0}$ is
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The value of $sin^{2}1^{0} + sin^{2}2^{0} + sin^{2}3^{0}+.........+sin^{2}89^{0}$ is
1). 22
2). 44
3). $22\frac{1}{2}$
4). $44\frac{1}{2}$
2 answers
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it from previous year ssc papers, $44\frac{1}{2}$ is the right answer
2 vote
sin2 1° + sin2 2° + sin2 3° +..... + sin2 89°
= (sin2 1° + sin2 89°) + (sin2 2° +sin2 88°) + .... to 44 terms + sin245°
= (sin2 1° + sin2 (90° – 1°) + (sin22° + sin2 (90° – 2°) +....to 44terms + $\frac{1}{\sqrt{2}}$
= (sin2 1° +cos2 1°) +(sin2 2° +cos2 2°) + ....to 44 terms +$\frac{1}{2}$
= 1 + 1 + ....to 44 terms +$\frac{1}{2}$
= 44 +$\frac{1}{2}$ = 44$\frac{1}{2}$ .