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Question
Find the value of sin105°.
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Solution
sin105° = sin(60° + 45°)
sin(A + B) = sinAcosB + cosAsinB
sin(60° + 45°) = sin60°cos45° + cos45°sin 60°
= `sqrt3/2*1/sqrt2 + 1/2*1/sqrt2`
= `sqrt3/(2sqrt2) + 1/(2sqrt2)`
= `(sqrt3 + 1)/(2sqrt2)`
sin(105°) = `(sqrt3 + 1)/(2sqrt2)`
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