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Answers to Senior High School Mathematics Textbooks published by People's Education Press
( 1)(sin2α-cos2α)^2=sin2α^2+cos2α^2-2sin2αcos2α= 1-sin4α;

(3) 2 tanx = 4 tanx/2/(1-tanx/2 2

tan(x/2+π/4)+tan(x/2-π/4)=(tanx/2+ 1)/( 1-tanx/2)+(tanx/2- 1)/( 1+tanx/2)

=4tanx/2/( 1-tanx/2^2);

⑸( 1-2sinαcosα)/(cosα^2-sinα^2)=(sinα^2+cosα^2-2sinαcosα)/(cosα^2-sinα^2)

=(cosα-sinα)^2/(cosα-sinα)(cosα+sinα)=cosα-sinα/cosα+sinα

=( 1-sinα/cosα)/( 1+sinα/cosα)/=( 1-tanα)/( 1+tanα);

(7)( 1-cos2θ)/( 1+cos2θ)={ 1-(2cosθ^2- 1)}/{ 1+(2cosθ^2- 1)}=(2-2cosθ^2)/2cosθ^2

=2sinθ^2/2cosθ^2=tanθ^2