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\operatorname { sin } 10 ^ { \circ } + \operatorname { sin } 20 ^ { \circ } + \operatorname { sin } 40 ^ { \circ } + \operatorname { sin } 50 ^ { \circ } = \operatorname { sin } 70 ^ { \circ } + \operatorname { sin } 80 ^ { \circ } |
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Answer» L.H.S. = 2sin15cos5+2sin45cos5 [ using sin C+sin D= 2sin C+D/2 cos C-D/2 for sin10+sin20 & sin40+sin50]= 2cos5 (sin15+sin45)= 2cos5 (2sin30cos15) [ using sin C+sin D= 2sin C+D/2 cos C-D/2 ]= 2cos5 (2 x 1/2 x cos15)= 2cos5 cos15 R.H.S. = sin70+sin80= 2sin75cos5 [ using sin C+sin D= 2sin C+D/2 cos C-D/2 ] sin75 = sin(90-15) = cos 15 L.H.S = 2cos5 cos15R.H.S. = 2cos15 cos5 [ since, sin75 = cos15 ] |
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