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प्रश्न
Evaluate the following
tan2 30° + tan2 60° + tan2 45°
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उत्तर
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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= `(square + square)/(square xx square)` .....`[∵ square + square = 1]`
= `1/(square xx square)`
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= R.H.S.
∴ L.H.S. = R.H.S.
∴ cot θ + tan θ = cosec·sec θ
