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Question
Evaluate the Following
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45°
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Solution
4(sin4 60° + cos4 30°) − 3(tan2 60° − tan2 45°) + 5 cos2 45° ........(i)
By trigonometric ratios we have
`sin 60^@ = sqrt3/2 - cos 30^@(sqrt3/2) tan 60^@ = sqrt3 tan 45^@ = 1 cos 45^@ = 1/sqrt2`
By substituting above values in (i), we get
`4([sqrt3/2]^4) + [sqrt3/2]^4) - 3([3]^2 - [1]^2) + `5[1/sqrt2]^2`
`=> 4[9/16 + 9/16] - 3[3 - 1]+ 5[1/2]`
`=> 4. 18/16 - 6 + 5/2`
`=> 1/4 - 6 + 5/2`
`=> 1/4 - 6 + 5/2`
`= 9/2 + 5/2 - 6`
`= 14/2 - 6 = 7 - 6 = 1`
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