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bika2016p2z0ub
@bika2016p2z0ub
July 2022
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tg^2a+ctg^2a-6/tg^2a+ctg^2a+2
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sedinalana
Tg^2a+ctg^2a-6=sin²a/cos²a+cos²a/sin²a -6=
=(1-cos2a)/(1+cos2a) +(1+cos2a)/(1-cos2a) - 6=
=(1-2cos2a+cos²2a+1+2cos2a+cos²2a -6+6cos²2a)/(1-cos²2a)=
=(8cos²2a-4)/(1-cos²2a)=4(2cos²2a-1)/sin²2a=4cos4a/sin²2a
Tg^2a+ctg^2a + 2=sin²a/cos²a+cos²a/sin²a +2=
=(1-cos2a)/(1+cos2a) +(1+cos2a)/(1-cos2a) + 2=
=(1-2cos2a+cos²2a+1+2cos2a+cos²2a + 2- 2cos²2a)/(1-cos²2a)=
=4/(1-cos²2a)=4/sin²2a
(Tg^2a+ctg^2a - 6)/(Tg^2a+ctg^2a + 2)=4cos4a/sin²a:4/sin²a=
=4cos4a/sin²2a * sin²2a/4=cos4a
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Answers & Comments
=(1-cos2a)/(1+cos2a) +(1+cos2a)/(1-cos2a) - 6=
=(1-2cos2a+cos²2a+1+2cos2a+cos²2a -6+6cos²2a)/(1-cos²2a)=
=(8cos²2a-4)/(1-cos²2a)=4(2cos²2a-1)/sin²2a=4cos4a/sin²2a
Tg^2a+ctg^2a + 2=sin²a/cos²a+cos²a/sin²a +2=
=(1-cos2a)/(1+cos2a) +(1+cos2a)/(1-cos2a) + 2=
=(1-2cos2a+cos²2a+1+2cos2a+cos²2a + 2- 2cos²2a)/(1-cos²2a)=
=4/(1-cos²2a)=4/sin²2a
(Tg^2a+ctg^2a - 6)/(Tg^2a+ctg^2a + 2)=4cos4a/sin²a:4/sin²a=
=4cos4a/sin²2a * sin²2a/4=cos4a