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Question
Evaluate the Following
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60°
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Solution
4(sin4 30° + cos2 60°) − 3(cos2 45° − sin2 90°) − sin2 60° .....(i)
By trigonometric ratios we have
`sin 30^@ = 1/2 cos 60^@ = 1/2 cos 45^@ = 1/sqrt2 sin 90^@ = 1 sin 60^@ = sqrt3/2`
By substituting above values in (i), we get
`(4[(1/2)^4 + (1/2)^2]) - 3[[1/sqrt2]^2 - 1] - [sqrt3/2]^2`
`4[1/16 + 1/4] - 3[(1 - [sqrt2])/(sqrt2)^2] - 3/4`
`= 1/4 + 1 - 3/4 + 3/2 = 2`
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