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![frac{4sin80*sin10}{sin20}=frac{frac{4(cos(80-10)-cos(80+10))}{2}}{sin20}
frac{2(cos70-cos90)}{sin20}=frac{2(cos(70-90))}{sin20} \
frac{2(cos70cos90+sin70sin90)}{sin20}= \
frac{2(sin70)}{sin20} \
frac{2(sin(90-20)}{sin20}= \
frac{2(sin90cos20-cos90sin20)}{sin20}= \
frac{2cos20}{sin20}](https://tex.z-dn.net/?f=frac%7B4sin80%2Asin10%7D%7Bsin20%7D%3Dfrac%7Bfrac%7B4%28cos%2880-10%29-cos%2880%2B10%29%29%7D%7B2%7D%7D%7Bsin20%7D+%0Afrac%7B2%28cos70-cos90%29%7D%7Bsin20%7D%3Dfrac%7B2%28cos%2870-90%29%29%7D%7Bsin20%7D+%5C+%0Afrac%7B2%28cos70cos90%2Bsin70sin90%29%7D%7Bsin20%7D%3D+%5C+%0Afrac%7B2%28sin70%29%7D%7Bsin20%7D+%5C+%0Afrac%7B2%28sin%2890-20%29%7D%7Bsin20%7D%3D+%5C%0Afrac%7B2%28sin90cos20-cos90sin20%29%7D%7Bsin20%7D%3D+%5C%0Afrac%7B2cos20%7D%7Bsin20%7D+%0A%0A "frac{4sin80*sin10}{sin20}=frac{frac{4(cos(80-10)-cos(80+10))}{2}}{sin20}
frac{2(cos70-cos90)}{sin20}=frac{2(cos(70-90))}{sin20} \
frac{2(cos70cos90+sin70sin90)}{sin20}= \
frac{2(sin70)}{sin20} \
frac{2(sin(90-20)}{sin20}= \
frac{2(sin90cos20-cos90sin20)}{sin20}= \
frac{2cos20}{sin20}")
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