Rút gọn biểu thức A = sin^2 30 – sin^ 40 – sin^2 50 + sin^2 60 B = cos^2 25 – cos^2 35 + cos^2 45 – cos^2 55 + cos^2 65

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1. $A=\sin^230^o+\sin^260^-(\sin^240^o+\sin^250^o)$

   $=\sin^230^o+\cos^230^o-(\sin^240^o+\cos^240^o)$

   $=1-1=0$

   $B=\cos^225^o+\cos^265^o-(\cos^235^o+\cos^255^o)+\cos^245^o$

   $=\cos^225^o+\sin^225^o-(\sin^255^o+\cos^255^o)+(\dfrac{1}{\sqrt2})^2$

   $=1-1+\dfrac{1}{2}$

   $=\dfrac{1}{2}$

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2. Đáp án:

    

   Giải thích các bước giải:

   `A = sin^2 30^o- sin^2 40^o – sin^2 50^o + sin^2 60^o`

   `A=sin^2 30^o- sin^2 40^o – cos^2 40^o + cos^2 30^o`

   `A=(sin^2 30^o + cos^2 30^o) – (sin^2 40^o + cos^2 40^o)`.

   `A=1-1`

   `A=0`.

   `B = cos^2 25^o – cos^2 35^o + cos^2 45^o – cos^2 55^o + cos^2 65^o`

   `B = cos^2 25^o – cos^2 35^o + cos^2 45^o – sin^2 35^o + sin^2 25^o`

   `B = (cos^2 25^o + sin^2 25^o) – (cos^2 35^o + sin^2 35^o) + cos^2 45^o`

   `B = 1 – 1 + 1/2`

   `B=1/2`.

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