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Question
Evaluate the following
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°`
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Solution
`sin^2 30° cos^2 45 ° + 4 tan^2 30° + 1/2 sin^2 90° − 2 cos^2 90° + 1/24 cos^2 0°` ....(i)
By trigonometric ratios we have
`sin 30^@ = 1/2` `cos 45^@ = 1/sqrt2` `tan 30^2 = 1/sqrt3` `sin 90^@ = 1 cos 90^@ = 0 cos 0^@ = 1`
By substituting above values in (i), we get
`[1/2]^2 . [1/sqrt2]^2 + 4[1/sqrt3]^2 + 1/2[1]^2 - 2[0]^2 + 1/24 [1]^2`
`1/4.1/2 + 4/ 1/3 + 1/2 - 0 + 1/24`
`1/8 + 4/3 + 1/2 + 1/24 = 48/24 = 2`
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