Question

rút gọn biểu thức A = (tan²a - sin²a) / (cot²a - cos²a) là bao nhiêu ?

Answer 1

\(A=\dfrac{tan^2a-sin^2a}{cot^2a-cos^2a}\)

\(A=\dfrac{\dfrac{sin^2a}{cos^2a}-sin^2a}{\dfrac{cos^2a}{sin^2a}-cos^2a}=\dfrac{sin^2a\left(\dfrac{1}{cos^2a}-1\right)}{cos^2a\left(\dfrac{1}{sin^2a}-1\right)}\)

\(A=\dfrac{sin^2a\left(\dfrac{1-cos^2a}{cos^2a}\right)}{cos^2a\left(\dfrac{1-sin^2a}{sin^2a}\right)}=\dfrac{sin^2a\left(\dfrac{sin^2a}{cos^2a}\right)}{cos^2a\left(\dfrac{cos^2a}{sin^2a}\right)}\)

\(A=\dfrac{\dfrac{sin^4a}{cos^2a}}{\dfrac{cos^4a}{sin^2a}}=\dfrac{sin^4a}{cos^2a}.\dfrac{sin^2a}{cos^4a}\)

\(A=\dfrac{sin^6a}{cos^6a}=tan^6a\)