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Question
Express the following as a product
sin 75° sin 35°
Solution
We know sin C – sin D = `2 cos ("C" + "D")/2 * sin ("C" - "D")/2`
Take C = 75°, D = 35°
sin 75° – sin 35° = `2cos((75^circ + 35^circ)/2) * sin((75^circ - 35^circ)/2)`
sin 75° – sin 35° = `2cos(110^circ/2) * sin(40^circ/2)`
sin 75° – sin 35° = 2 cos 55° sin 20°
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`1/(cos 80^circ) - sqrt(3)/(sin 80^circ)` =
