Question

find the value of
$sin {}^{2} 1degree +sin {}^{2} 3 degree + sin {}^{2} 5degree + .... + sin {}^{2} 87degree + sin {}^{2} 89 degree$

Answer 1

$\: \: \: \: \: { \sin}^{2}1degree + { \sin }^{2}3degree....... { \sin }^{2}87degree + { \sin }^{2}89degree \\ = { \sin }^{2}1degree + { \sin }^{2}3degree........ { \sin}^{2}(90 - 3) + { \sin }^{2}(90 - 1) \\ = \sin ^{2} 1degree + { \cos }^{2}1degree + { \sin }^{2} 3degree + { \cos}^{2}3degree + ......... \\ = 1 + 1.....45times \\ = 1 \times 45 \\ = 45.$




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