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F.4 TRIGONOMETRY M2
1. PROVE THATsin(32+a)cos(58-b)+cos(32+a)sin(58-b) = cos(a-b) 2.PROVE THAT sin(2a+b)/sina - 2cos(a+b) = sinb/sina 3. PROVE THAT tan(45+θ)+tan(45-θ) = 2/cos^2θ-sin^2θ
最佳解答:
1 Let x = 32 + a, y = 58 - b sin(32+a)cos(58-b)+cos(32+a)sin(58-b) = sinxcosy+cosxsiny = sin(x + y) = sin(32 + a + 58 - b) = sin(90 + a - b) =cos(a - b) 2 sin(2a + b)/sina - 2cos(a + b) = (sin2acosb + cos2asinb)/sina - 2cos(a + b) = (2sinacosacosb + sinb - 2sin^2asinb)/sina - 2cos(a + b) = (2sinacos(a + b) + sinb)/sina - 2cos(a + b) = sib/sina 3 tan(45+θ)+tan(45-θ) = (tan45 + tanθ)/(1 - tan45tanθ) + (tan45 - tanθ)/(1 + tan45tanθ) = (1 + tanθ)/(1 - tanθ) + (1 - tanθ)/(1 + tanθ) = (cosθ + sinθ)/(cosθ - sinθ) + (cosθ - sinθ)/(cosθ + sinθ) = 2/(cos^2θ - sin^2θ)
其他解答:
F.4 TRIGONOMETRY M2
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發問:1. PROVE THATsin(32+a)cos(58-b)+cos(32+a)sin(58-b) = cos(a-b) 2.PROVE THAT sin(2a+b)/sina - 2cos(a+b) = sinb/sina 3. PROVE THAT tan(45+θ)+tan(45-θ) = 2/cos^2θ-sin^2θ
最佳解答:
1 Let x = 32 + a, y = 58 - b sin(32+a)cos(58-b)+cos(32+a)sin(58-b) = sinxcosy+cosxsiny = sin(x + y) = sin(32 + a + 58 - b) = sin(90 + a - b) =cos(a - b) 2 sin(2a + b)/sina - 2cos(a + b) = (sin2acosb + cos2asinb)/sina - 2cos(a + b) = (2sinacosacosb + sinb - 2sin^2asinb)/sina - 2cos(a + b) = (2sinacos(a + b) + sinb)/sina - 2cos(a + b) = sib/sina 3 tan(45+θ)+tan(45-θ) = (tan45 + tanθ)/(1 - tan45tanθ) + (tan45 - tanθ)/(1 + tan45tanθ) = (1 + tanθ)/(1 - tanθ) + (1 - tanθ)/(1 + tanθ) = (cosθ + sinθ)/(cosθ - sinθ) + (cosθ - sinθ)/(cosθ + sinθ) = 2/(cos^2θ - sin^2θ)
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