a) \(B=\dfrac{sin^4x-cos^4x+cos^2x}{2\left(1-cosx\right)\left(1+cosx\right)}\)
\(B=\dfrac{\left(sin^2x\right)^2-\left(cos^2x\right)^2+cos^2x}{2\left(1-cos^2x\right)}\)
\(B=\dfrac{\left(sin^2x-cos^2x\right)\left(sin^2x+cos^2x\right)+cos^2x}{2\left(sin^2x+cos^2x-cos^2x\right)}\)
\(B=\dfrac{sin^2x-cos^2x+cos^2x}{2sin^2x}=\dfrac{sin^2x}{2sin^2x}=\dfrac{1}{2}\)
b) \(\dfrac{1+sin2x-cos2x}{1+sin2x+cos2x}=tanx\)
\(VT=\dfrac{1+2sinx.cosx-\left(1-2sin^2x\right)}{1+2sinx.cosx+2cos^2x-1}\)
\(VT=\dfrac{1+2sinx.cosx-1+2sin^2x}{2sinx.cosx+2cos^2x}\)
\(VT=\dfrac{2sinx.cosx+2sin^2x}{2sinx.cosx+2cos^2x}\)
\(VT=\dfrac{2sinx\left(cosx+sinx\right)}{2cosx\left(sinx+cosx\right)}=\dfrac{sinx}{cosx}=tanx=VP\) ( đpcm )
p/s : sửa \(cos1x\rightarrow cos2x\)
