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Question
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
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Solution
tan2 30° + tan2 60° + tan2 45° ....(i)
By trigonometric ratios we have
`tan 30^@ = 1/sqrt3 tan 60^@ = sqrt3 tan 45^@ = 1`
By substituting above values in (i), we get
`[1/sqrt3]^2 + [sqrt3]^2 + [1]^2`
`=> 1/3 + 3 + 1 => 1/3 + 4`
`=> (1 + 12)/3 = 13/3`
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