Question

cosx=-4/5 x属于(π,3π/2)求1+tanx/2除以1-tanx/2

Answer 1

cosx=-4/5

x∈(π,3π/2)

sinx=-√[1-(-4/5)^2]=-3/5

所以[1+tan(x/2)]/[1-tan(x/2)]

=[cos(x/2)+sin(x/2)]/[cos(x/2)-sin(x/2)](分子分母同时乘以cos(x/2))

=[cos(x/2)+sin(x/2)]^2/[cos(x/2)-sin(x/2)][cos(x/2)+sin(x/2)]

=(1+sinx)/cosx

=(1-3/5)/(-4/5)

=-1/2

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