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Question
Prove that: `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3 = 10`
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Solution
Left side = `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3`
= `2sin^2(pi-pi/4)+2xx(1/sqrt2)^2 + 2 xx (2)^2`
(∵ cos `pi/4 = 1/sqrt2,sec pi/3=2`)
= `2 sin^2 pi/4+2/2+ xx4` [∵ sin `(pi-θ)`=sin θ]
= 2 x `(1/sqrt2)^2 + 2/2` + 8
(∵ `sin pi/4 = 1/sqrt2`)
= `2/2`+ 1 + 8
= 10 = Right side.
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