\(A=cot^2a-sin^2a.cot^2a+1-cot^2a\)
\(=1-sin^2a.cot^2a=1-sin^2a.\dfrac{cos^2a}{sin^2a}\)
\(=1-cos^2a=sin^2a\)
\(B=\dfrac{2cos^2a-\left(sin^2a+cos^2a\right)}{sina+cosa}=\dfrac{cos^2a-sin^2a}{sina+cosa}\)
\(=\dfrac{\left(cosa-sina\right)\left(cosa+sina\right)}{sina+cosa}\)
\(=cosa-sina\)
\(C=\left(1+\dfrac{cosa}{sina}\right)sin^3a+\left(1+\dfrac{sina}{cosa}\right)cos^3a\)
\(=\left(sina+cosa\right)sin^2a+\left(sina+cosa\right)cos^2a\)
\(=\left(sina+cosa\right)\left(sin^2a+cos^2a\right)\)
\(=sina+cosa\)
\(D=\dfrac{sin^2a-\dfrac{sin^2a}{cos^2a}}{cos^2a-\dfrac{cos^2a}{sin^2a}}=\dfrac{sin^2a}{cos^2a}.\dfrac{sin^2a\left(cos^2a-1\right)}{cos^2a\left(sin^2a-1\right)}\)
\(=\dfrac{sin^4a\left(-sin^2a\right)}{cos^4a.\left(-cos^2a\right)}=\dfrac{sin^6a}{cos^6a}\)
\(=tan^6a\)
\(E=\dfrac{sin^2a+cos^2a+2sina.cosa-1}{\dfrac{cosa}{sina}-sina.cosa}=\dfrac{2sina.cosa.sina}{cosa-cosa.sin^2a}\)
\(=\dfrac{2sin^2a.cosa}{cosa.\left(1-sin^2a\right)}=\dfrac{2sin^2a}{cos^2a}\)
\(=2tan^2a\)
\(F=\dfrac{1}{sin^2a}-cos^2a-sin^2a\)
\(=1+cot^2a-\left(sin^2a+cos^2a\right)\)
\(=cot^2a\)
Câu G trùng câu B
\(H=sin^2a\left(1+\dfrac{cosa}{sina}\right)+cos^2a\left(1+\dfrac{sina}{cosa}\right)\)
\(=sin^2a+sina.cosa+cos^2a+cosa.sina\)
\(=sin^2a+cos^2a+2sina.cosa\)
\(=1+sin2a\)
\(I=cos^2a\left(1+cot^2a\right)=cos^2a\left(1+\dfrac{cos^2a}{sin^2a}\right)\)
\(=\dfrac{cos^2a\left(sin^2a+cos^2a\right)}{sin^2a}=cot^2a\)
\(J=sin^2a\left(1+tan^2a\right)=sin^2a\left(1+\dfrac{sin^2a}{cos^2a}\right)\)
\(=\dfrac{sin^2a\left(sin^2a+cos^2a\right)}{cos^2a}=\dfrac{sin^2a}{cos^2a}\)
\(=tan^2a\)
K trùng G trùng B
