证明tan(x/2+45°)+tan(x/2-45°)=2tanx,
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证明tan(x/2+45°)+tan(x/2-45°)=2tanx,
tan(x/2+45°)+tan(x/2-45°)
=[tan(x/2)+tan45°]/[1-tan(x/2)tan45°]
+[tan(x/2)-tan45°]/[1+tan(x/2)tan45°]
=[tan(x/2)+1]/[1-tan(x/2)]+[tan(x/2)-1]/[1+tan(x/2)]
={[tan(x/2)+1]^2-[tan(x/2)-1]^2}/{1-[tan(x/2)]^2}
=4tan(x/2)/{1-[tan(x/2)]^2}
=2tanx.
=[tan(x/2)+tan45°]/[1-tan(x/2)tan45°]
+[tan(x/2)-tan45°]/[1+tan(x/2)tan45°]
=[tan(x/2)+1]/[1-tan(x/2)]+[tan(x/2)-1]/[1+tan(x/2)]
={[tan(x/2)+1]^2-[tan(x/2)-1]^2}/{1-[tan(x/2)]^2}
=4tan(x/2)/{1-[tan(x/2)]^2}
=2tanx.
证明tan(x/2+45°)+tan(x/2-45°)=2tanx,
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