求证这两道题目!

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求证这两道题目!
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求证这两道题目!
求证这两道题目!

求证这两道题目!
1.
tan²x+1/tan²x
=sin²x/cos²x+cos²x/sin²x
=(sin⁴x+cos⁴x)/(sin²xcos²x)
=[(sin²x+cos²x)²-2sin²xcos²x]/(sin²xcos²x)
=[1-½sin²(2x)]/[¼sin²(2x)]
=[8-4sin²(2x)]/[2sin²(2x)]
={8-2[1-cos(4x)]}/[1-cos(4x)]
=[6+2cos(4x)]/[1-cos(4x)]
=2(3+cos4x)/(1-cos4x)
2.
sinβ=msin(2α+β)
sin[(α+β)-α]=msin[(α+β)+α]
sin(α+β)cosα-cos(α+β)sinα=msin(α+β)cosα+mcos(α+β)sinα
等式两边同除以cos(α+β)cosα
tan(α+β)-tanα=mtan(α+β)+mtanα
(1-m)tan(α+β)=(1+m)tanα
tan(α+β)=[(1+m)/(1-m)]tanα