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Prove that 2sin^2((3pi)/4)+2cos^2(pi/4)+...

Prove that `2sin^2((3pi)/4)+2cos^2(pi/4)+2sec^2(pi/3)=10`

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sin (3 pi)/(4)=sin (135^(circ))=sin (90^(circ)+45^(circ))=cos 45^(circ)=(1)/(sqrt(2)).
.cos (pi)/(4)=(1)/(sqrt(2)), sec (pi)/(3)=2.
.2 sin ^(2) (3 pi)/(4)+2 cos ^(2) (pi)/(4)+2 sec ^(2) . (pi)/(3)=2 xx((1)/(sqrt(2)))^(2)+2 xx((1)/(sqrt(2)))^(2)+2 xx(2)^(2).
.=2 xx (1)/(2)+2 xx (1)/(2)+8=10.
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