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July 2022
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sedinalana
Verified answer
Tga=2
cos²a=1:(1+tg²a)=1:(1+4)=1/5
cosa=1/√5
sina=√(1-cos²a)=√(1-1/5)=2/√5
cos2a=cos²a-sin²a=1/5-4/5=-3/5
sin2a=2sinacosa=2*2/√5*1/√5=4/5
tg2a=sin2a/cos2a=4/5:(-3/5)=-4/3
(2-5cos2a)/(6+10sin2a)-(13+3tg2a)/(10cos2a-15sin2a)=
=(2+3)/(6+8)-(13-4)/(-6-12)=5/14+9/18=5/14+1/2=5/14+7/14=12/14=6/7
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Answers & Comments
Verified answer
Tga=2cos²a=1:(1+tg²a)=1:(1+4)=1/5
cosa=1/√5
sina=√(1-cos²a)=√(1-1/5)=2/√5
cos2a=cos²a-sin²a=1/5-4/5=-3/5
sin2a=2sinacosa=2*2/√5*1/√5=4/5
tg2a=sin2a/cos2a=4/5:(-3/5)=-4/3
(2-5cos2a)/(6+10sin2a)-(13+3tg2a)/(10cos2a-15sin2a)=
=(2+3)/(6+8)-(13-4)/(-6-12)=5/14+9/18=5/14+1/2=5/14+7/14=12/14=6/7