Question

Chứng minh rằng:

\(\dfrac{4sin^2\left(a\right)}{1-cos^2\left(\dfrac{a}{2}\right)}=16cos^2\left(\dfrac{a}{2}\right)\)

Answer 1

\(VT=\dfrac{4sina.sina}{1-cos^2\dfrac{a}{2}}=\dfrac{4.2sin\dfrac{a}{2}cos\dfrac{a}{2}.2sin\dfrac{a}{2}cos\dfrac{a}{2}}{1-cos^2\dfrac{a}{2}}=\dfrac{16sin^2\dfrac{a}{2}cos^2\dfrac{a}{2}}{1-cos^2\dfrac{a}{2}}\)

Mà \(sin^2\dfrac{a}{2}+cos^2\dfrac{a}{2}=1\Rightarrow cos^2\dfrac{a}{2}=1-sin^2\dfrac{a}{2}\)

\(\Rightarrow VT=\dfrac{16sin^2\dfrac{a}{2}cos^2\dfrac{a}{2}}{1-\left(1-sin^2\dfrac{a}{2}\right)}=\dfrac{16sin^2\dfrac{a}{2}cos^2\dfrac{a}{2}}{sin^2\dfrac{a}{2}}=16cos^2\dfrac{a}{2}=VP\)

\(\Rightarrowđpcm\)

Answer 2