求证:1+2sina cosa /sin^2a -cos^2a = tana +1/tana -1.
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求证:1+2sina cosa /sin^2a -cos^2a = tana +1/tana -1.
左式=(1+sin2α)/(-cos2α)(倍角公式)
=(1+2tanα/(1+tan²α))/-(1-tan²α)/(1+tan²α))(万能公式)
=((1+tan²α+2tanα)/-(1+tan²α))/(1-tan²α)/(1+tan²α))
=(1+tanα)²/-(1-tan²α)
=(1+tanα)²/-((1-tanα)(1+tanα))
=(1+tanα)/-(1-tanα)
=(tanα+1)/(tanα-1)
=右式
=(1+2tanα/(1+tan²α))/-(1-tan²α)/(1+tan²α))(万能公式)
=((1+tan²α+2tanα)/-(1+tan²α))/(1-tan²α)/(1+tan²α))
=(1+tanα)²/-(1-tan²α)
=(1+tanα)²/-((1-tanα)(1+tanα))
=(1+tanα)/-(1-tanα)
=(tanα+1)/(tanα-1)
=右式
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