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प्रश्न
Evaluate the following
sin2 30° + sin2 45° + sin2 60° + sin2 90°
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उत्तर
sin2 30° + sin2 45° + sin2 60° + sin2 90° .....(1)
`sin 30^@ = 1/2 sin 45^@ = 1/sqrt2`
`sin 60^@ = sqrt3/2 sin 90^@ = 1`
By substituting above values in (i), we get
`= [1/2]^2 + [1/sqrt2]^2 + [sqrt3/2]^2 + [1]^2`
`= 1/4 + 1/2 + 3/4 + 1 => (1 + 3)/4 + (1 + 2)/2`
`=> 1 + 3/2 = (2 + 3)/2 = 5/2`
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