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Question
Evaluate the Following
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@`
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Solution
`4/(cot^2 30^@) + 1/(sin^2 60^@) - cos^2 45^@` .....(i)
By trigonometric ratios we have
`cot 30^@ = sqrt3 sin 60^@ = sqrt3/2 cos 45^@ = 1/sqrt2`
By substituting above values in (i), we get
`4/(sqrt3)^2 + 1/(sqrt3/2)^2 - (1/sqrt2)^2`
`4/3 + 4/3 - 1/2 = 13/6`
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