sin^2 (((7π)/8))+sin^2 (((3π)/8))+sin^2 (((5π)/8))+sin^2 ((π/8)) ?


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Question Number 90700 by jagoll last updated on 25/Apr/20

$\sin^{2} (\frac{7 π}{8}) + \sin^{2} (\frac{3 π}{8}) + \sin^{2} (\frac{5 π}{8}) + \sin^{2} (\frac{π}{8}) ?$
Commented by john santu last updated on 25/Apr/20
$sin^2 (((7π)/8)) = sin^2 (π−((7π)/8)) = sin^2 ((π/8)) sin^2 (((5π)/8)) = sin^2 (π−((5π)/8)) = sin^2 (((3π)/8)) ⇒ 2 { sin^2 (((3π)/8)) + sin^2 ((π/8))} = 2 { sin^2 (((3π)/8)) + cos^2 ((π/2)−(π/8))} = 2 { sin^2 (((3π)/8)) + cos^2 (((3π)/8))} = 2 .$
$\sin^{2} (\frac{7 π}{8}) = \sin^{2} (π - \frac{7 π}{8}) = \sin^{2} (\frac{π}{8})$ $\sin^{2} (\frac{5 π}{8}) = \sin^{2} (π - \frac{5 π}{8}) = \sin^{2} (\frac{3 π}{8})$ $\Rightarrow 2 {\sin^{2} (\frac{3 π}{8}) + \sin^{2} (\frac{π}{8})}$ $= 2 {\sin^{2} (\frac{3 π}{8}) + \cos^{2} (\frac{π}{2} - \frac{π}{8})}$ $= 2 {\sin^{2} (\frac{3 π}{8}) + \cos^{2} (\frac{3 π}{8})}$ $= 2 .$
Commented by jagoll last updated on 25/Apr/20

$t h a n k y o u$
Commented by peter frank last updated on 26/Apr/20

$t h a n k s$
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