Question #d87b9

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Question #d87b9

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Answer 1 · 2016-12-18T18:19:59

$L H S = {cos}^{2} (\frac{π}{8}) + {cos}^{2} (\frac{3 π}{8}) + {cos}^{2} (\frac{5 π}{8}) + {cos}^{2} (\frac{7 π}{8})$ $LHS=Cos^2 (pi/8)+cos^2 ((3pi)/8)+cos^2 ((5pi)/8)+ cos^2 ((7pi)/8 )$

$= {cos}^{2} (\frac{π}{8}) + {cos}^{2} (\frac{π}{2} - \frac{π}{8}) + {cos}^{2} (\frac{5 π}{8}) + {cos}^{2} (\frac{3 π}{2} - \frac{5 π}{8})$ $=Cos^2( pi/8)+cos^2(pi/2-pi/8)+cos^2 ((5pi)/8)+ cos^2 ((3pi)/2-(5pi)/8 )$

$= {cos}^{2} (\frac{π}{8}) + {(- sin (\frac{π}{8}))}^{2} + {cos}^{2} (\frac{5 π}{8}) + {sin}^{2} (\frac{5 π}{8})$ $=Cos^2( pi/8)+(-sin(pi/8))^2+cos^2 ((5pi)/8)+ sin^2 ((5pi)/8 )$

$= {cos}^{2} (\frac{π}{8}) + {sin}^{2} (\frac{π}{8}) + {cos}^{2} (\frac{5 π}{8}) + {sin}^{2} (\frac{5 π}{8})$ $=Cos^2( pi/8)+sin^2(pi/8)+cos^2 ((5pi)/8)+ sin^2 ((5pi)/8 )$

$= 1 + 1 = 2 = R H S$ $=1+1=2=RHS$

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Question #d87b9

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