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Question
Evaluate:
sin 50° – sin 70° + sin 10°
Solution
LHS = (sin 50° – sin 70°) + sin 10°
= 2 cos `((50^circ + 70^circ)/2) sin ((50^circ - 70^circ)/2)` + sin 10°
`[∵ sin "C" - sin "D" = 2 cos (("C + D")/2) sin (("C - D")/2)]`
= 2 cos 60° sin(-10°) + sin 10°
`= 2 xx 1/2` (-sin 10°) + sin 10° ...[∵ sin(-θ) = -sin θ]
= -sin 10° + sin 10°
= 0
= RHS
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