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Question

sin20°+sin25°+sin210°+....sin290° is equal to

A
18
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B
9
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C
13
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D
192
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Solution

The correct option is D 192
sin20°+sin25°+sin210°+...+sin285°+sin290°

=(sin20°+sin290°)+(sin25°+sin285°)+...+(sin235°+sin255°)+(sin240°+sin250°)+sin245°

=(sin20°+cos20°)+(sin25°+cos25°)+...+(sin235°+cos235°)+(sin240°+cos240°)+sin245°

=[1+1+.....+1]+(12)2

where 0°,5°,10°,...40° total 9 terms
Hence, 1+1+.....+1 for 9 terms =9

Final answer =9+12=192

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