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Question
Evaluate the following
cos2 30° + cos2 45° + cos2 60° + cos2 90°
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Solution
cos2 30° + cos2 45° + cos2 60° + cos2 90° ....(i)
By trigonometric ratios we have
`cos 30^@ = sqrt3/2 cos 45^@ = 1/sqrt2`
`cos 60^@ = 1/2 cos 90^@ = 0`
By substituting above values in (i), we get
`[sqrt3/2]^2 + [1/sqrt2]^2 + [1/2]^2 + [1]^2`
`3/4 +1/2 + 1/4 = 0 => 1 + 1/2 = 3/2`
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