18 tháng 4 2022 lúc 20:14
a: cos^4a-sin^4a
=(cos^2a+sin^2a)(cos^2a-sin^2a)
=cos^2a-sin^2a
VP=\(\dfrac{1-tan^2a}{1+tan^2a}=\dfrac{1-\left(\dfrac{sina}{cosa}\right)^2}{1+\left(\dfrac{sina}{cosa}\right)^2}\)
\(=\left(1-\dfrac{sin^2a}{cos^2a}\right):\left(1+\dfrac{sin^2a}{cos^2a}\right)\)
\(=\dfrac{cos^2a-sin^2a}{cos^2a+sin^2a}=cos^2a-sin^2a\)=VT
b: \(\dfrac{sin^3a+cos^3a}{sina+cosa}\)
=(sina+cosa)(sin^2a+cos^2a-sina*cosa)/(sina+cosa)
=1-sina*cosa
c:tan^2a-sin^2a
=sin^2a(1/cos^2a-1)
\(=sin^2a\cdot\dfrac{1-cos^2a}{cos^2a}=tan^2a\cdot sin^2a\)
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