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sin80° sin65° sin35°÷sin20°+ sin50°+sin110° |
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Answer» Let us simplify step by step sin 80 = sin (90-10) = cos 10, sin 65 sin 35= 1/2( cos (65-35)- cos(65+35)= 1/2( cos 30 - cos 100), sin 80 sin 65 sin 35 = 1/2(cos 10 ( cos 30 - cos 100)) cos 100= cos (90+10) = sin 10. Therefore. = 1/2 cos 10 cos 30 -1/2 cos 10 sin 10= 1/4 (cos 40 + cos 20 ) -1/4 sin 20 This gives 96 sin 80 sin 65 sin 35 = 24 (- sin 20 + cos 20 + cos 40) Let us simplify the denominator. sin 50 = sin (90-40) = - cos 40 sin 110 = sin (90 +20) cos 20. This gives sin 20 + sin 50 + sin 110= sin 20 + cos 20 -cos40. It seems that there is sign mistake. You check it. You will get -24 or +24. |
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