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標題:
compound angles
發問:
solve the following equation for x (0 -360degree) tan(30+x) tan(30-x) = 1 - 2cos2x
tan(30*+x) tan(30*-x) = 1 - 2cos2x sin(30*+x)sin(30*-x)/cos(30*+x)cos(30*-x) = 1 - 2cos2x (1/2)(cos2x-cos60*)/(1/2)(cos60*+cos2x) = 1 - 2cos2x cos2x- 1/2 = (1-2cos2x)( 1/2 + cos2x ) cos2x-1/2 = 1/2+cos2x-cos2x-2cos22x 2cos22x+cos2x-1=0 (2cos2x-1)(cos2x+1)=0 cos2x=1/2 or cos2x=-1 2x = 60*, 300*,420*, 660* or 2x = 180*, 540* x = 30*, 150*, 210*, 330* or 90*, 270*
其他解答:8758B59A7FA1EEA7
compound angles
發問:
solve the following equation for x (0 -360degree) tan(30+x) tan(30-x) = 1 - 2cos2x
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最佳解答:tan(30*+x) tan(30*-x) = 1 - 2cos2x sin(30*+x)sin(30*-x)/cos(30*+x)cos(30*-x) = 1 - 2cos2x (1/2)(cos2x-cos60*)/(1/2)(cos60*+cos2x) = 1 - 2cos2x cos2x- 1/2 = (1-2cos2x)( 1/2 + cos2x ) cos2x-1/2 = 1/2+cos2x-cos2x-2cos22x 2cos22x+cos2x-1=0 (2cos2x-1)(cos2x+1)=0 cos2x=1/2 or cos2x=-1 2x = 60*, 300*,420*, 660* or 2x = 180*, 540* x = 30*, 150*, 210*, 330* or 90*, 270*
其他解答:8758B59A7FA1EEA7
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