Question

 

chứng minh các biểu thức ko phụ thuộc của x

Answer 1

\(\dfrac{sin4a}{1+cos4a}\cdot\dfrac{cos2a}{1+cos2a}\)

\(=\dfrac{2\cdot sin2a\cdot cos2a}{1+cos\left(2\cdot2a\right)}\cdot\dfrac{cos2a}{1+2\cdot cos^2a-1}\)

\(=\dfrac{2\cdot sin2a\cdot cos2a}{2\cdot cos^2a}\cdot\dfrac{cos2a}{1+2\cdot cos^22a-1}\)

\(=\dfrac{2\cdot sin2a\cdot cos2a}{2\cdot cos^2a}\cdot\dfrac{cos2a}{2\cdot cos^22a}\)

\(=\dfrac{sin2a}{cos2a}\cdot\dfrac{cos2a}{2\cdot cos^2a}=\dfrac{sin2a}{2\cdot cos^2a}=\dfrac{2\cdot sina\cdot cosa}{2\cdot cos^2a}=\dfrac{sina}{cosa}=tana\)