证明左右相等的三角函数题 (secX + tanX)^2 = (1+sinX) / (1-sinX).怎么证明它们相等?化简 ( X^2 - Y^2 )^2 + 4XY ( X + Y )^2
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![证明左右相等的三角函数题 (secX + tanX)^2 = (1+sinX) / (1-sinX).怎么证明它们相等?化简 ( X^2 - Y^2 )^2 + 4XY ( X + Y )^2](/uploads/image/z/11578762-10-2.jpg?t=%E8%AF%81%E6%98%8E%E5%B7%A6%E5%8F%B3%E7%9B%B8%E7%AD%89%E7%9A%84%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E9%A2%98+%28secX+%2B+tanX%29%5E2+%3D+%281%2BsinX%29+%2F+%281-sinX%29.%E6%80%8E%E4%B9%88%E8%AF%81%E6%98%8E%E5%AE%83%E4%BB%AC%E7%9B%B8%E7%AD%89%3F%E5%8C%96%E7%AE%80+%EF%BC%88+X%5E2+-+Y%5E2+%29%5E2+%2B+4XY+%28+X+%2B+Y+%29%5E2)
证明左右相等的三角函数题 (secX + tanX)^2 = (1+sinX) / (1-sinX).怎么证明它们相等?化简 ( X^2 - Y^2 )^2 + 4XY ( X + Y )^2
证明左右相等的三角函数题
(secX + tanX)^2 = (1+sinX) / (1-sinX)
.怎么证明它们相等?
化简 ( X^2 - Y^2 )^2 + 4XY ( X + Y )^2
证明左右相等的三角函数题 (secX + tanX)^2 = (1+sinX) / (1-sinX).怎么证明它们相等?化简 ( X^2 - Y^2 )^2 + 4XY ( X + Y )^2
(secX + tanX)^2 = (1+sinX) / (1-sinX)
(sec^2 x + 2secx*tan x+ tan^2 x)=(1+sin x)(1+sin x)/(1-sin x)(1+sin x)
(sec^2 x + 2*1/cos x * sin x/cos x + tan^2 x)=(1+sin x)^2/(1-sin^2 x)
(sec^2 x + 2 sin x/cos^2 x + tan^2 x)=(1+sin x)^2/cos^2 x
(1/cos^2 x + 2 sin x/cos^2 x + sin^2 x/cos^2 x)=(1+sin x)^2/cos^2 ((1+2sin x+sin ^2)/cos^2 x)=(1+sin x)^2/cos^2 x
(1+sin x)^2/cos^2 x=(1+sin x)^2/cos^2 x
左边= 右边
2.(x^2+y^2)^2-4xy(x^2+y^2)+4x^2y^2
=[(x^2+y^2)-2xy]^2
=[(x-y)^2]^2
左边=secx^2+tanx^a+2sec*tanx=1/(cosx^2)+(sinx^2)/(cosx^2)+2*1/(cosx)*(sinx)/(cosx)=(通分)(1+sinx^2+2sinx)/(cosx^2)
右边=[(1+sinx)*(1+sinx)]/[(1-sinx)*(1+sinx)]=(1+sinx^2+2sinx)/(1-sin^2)=(1+sinx^2+2sinx...
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左边=secx^2+tanx^a+2sec*tanx=1/(cosx^2)+(sinx^2)/(cosx^2)+2*1/(cosx)*(sinx)/(cosx)=(通分)(1+sinx^2+2sinx)/(cosx^2)
右边=[(1+sinx)*(1+sinx)]/[(1-sinx)*(1+sinx)]=(1+sinx^2+2sinx)/(1-sin^2)=(1+sinx^2+2sinx)/(cosx^2)(也就是分子分母同乘(1+sinx)再化解)
左边=右边
关键地方公式secx=1/cosx
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