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Question
Evaluate the following
sin 45° sin 30° + cos 45° cos 30°
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Solution
sin 45° sin 30° + cos 45° cos 30° …...(i)
We know that by trigonometric ratios we have,
`sin 45^@ = 1/sqrt2 sin 30^@ = 1/2`
`cos 45^@ = 1/sqrt2 cos 30^@ = sqrt3/2`
Substituting the values in (i) we get
`1/sqrt2 . 1/2 + 1/sqrt2 . sqrt3/2`
`= 1/sqrt2 . sqrt3/(2sqrt2) = (sqrt3 + 1)/(2sqrt2)`
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