求證:1/(sin10°)＾2 -3/(cos10°)＾2=32cos20°

熱心網(wǎng)友

證:(本題中省去角的單位:度)1/(sin10)^2-3/(cos10)^2=[(cod10)^2-3(sin10)^2]/(sin10cos10)^2=4(cos10-3sin10)(cos10+3sin10)/(2sin10cos10)^2=16(1/2*cos10-3/2*sin10)(1/2*cos10+3/2sin10)/(sin20)^2=16sin(30-10)sin(30+10)/(sin20)^2=16sin20sin40/(sin20)^2=16sin40/sin20=16*2sin20cos20/sin20=32cos20

熱心網(wǎng)友

證:(本題中省去角的單位:度)1/(sin10)^2-3/(cos10)^2=[(cod10)^2-3(sin10)^2]/(sin10cos10)^2=4(cos10-3sin10)(cos10+3sin10)/(2sin10cos10)^2=16(1/2*cos10-3/2*sin10)(1/2*cos10+3/2sin10)/(sin20)^2=16sin(30-10)sin(30+10)/(sin20)^2=16sin20sin40/(sin20)^2=16sin40/sin20=16*2sin20cos20/sin20=32cos20