倍角公式问题已知tanx=2,则tan2(x-π/4)等于A.4/3 B.-4/3 C.3/4 D.-3/4

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倍角公式问题已知tanx=2,则tan2(x-π/4)等于A.4/3 B.-4/3 C.3/4 D.-3/4

倍角公式问题已知tanx=2,则tan2(x-π/4)等于A.4/3 B.-4/3 C.3/4 D.-3/4
倍角公式问题
已知tanx=2,则tan2(x-π/4)等于
A.4/3 B.-4/3 C.3/4 D.-3/4

倍角公式问题已知tanx=2,则tan2(x-π/4)等于A.4/3 B.-4/3 C.3/4 D.-3/4
tan(x-π/4)
=(tanx-tanπ/4)/(1+tanxtanπ/4)
=(2-1)/(1+2)
=1/3
tan2(x-π/4)
=2tan(x-π/4)/(1-tan²(x-π/4))
=2×(1/3)/(1-(1/3)²)
=3/4

tan2(x-π/4)=tan(2x-π/2)=-tan(π/2-2x)=-cot2x=-[1-(tanx)^2]/(2tan2x)=-3/4
选D