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