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Question
Prove that `2 sin^2 (3pi)/4 + 2 cos^2 pi/4 + 2 sec^2 pi/3` = 10
Solution
`sin (3pi)/4 = sin 3 xx 45^circ = sin 135^circ`
= sin (180 - 45)
= sin 45° = `1/sqrt2`
`sec ((pi/3)) = 2`
`therefore 2 sin^2 ((3pi)/4) + 2 cos^2 pi/4 + 2 sec^2 pi/3`
`= 2 (sin (3pi)/4)^2 + 2 (cos pi/4)^2 + 2 (sec pi/3)^2`
`= 2 (1/sqrt2)^2 + 2 (1/sqrt2)^2 + 2 (2)^2`
`= cancel(2)(1/cancel(2)) + cancel(2)(1/cancel(2)) + 2 (2)^2`
= 1 + 1 + 8 = 10
Hence proved.
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