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Question
Prove the following :
sin 18° cos 39° + sin 6° cos 15° = sin 24° cos 33°
Solution
L.H.S. = sin 18°·cos 39° + sin 6°·cos 15°
= `1/2(2 cos 39^circ*sin18^circ + 2cos15^circ*sin6^circ)`
= `1/2[{sin(39^circ + 18^circ) - sin(39^circ - 18^circ)} + {sin(15^circ + 6^circ) - sin(15^circ - 6^circ)}]`
= `1/2[sin57^circ - sin21^circ + sin21^circ - sin9^circ]`
= `1/2(sin57^circ - sin9^circ)`
= `1/2 xx 2cos((57^circ + 9^circ)/2)*sin((57^circ - 9^circ)/2)`
= cos 33°·sin 24°
= sin 24°·cos 33°
= R.H.S.
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