\(B=\frac{sin126^0-cos144^0}{sin144^0-cos126^0}.tan36^0=\frac{cos36^0+sin54^0}{cos54^0+sin36^0}.tan36^0\)

\(=\frac{cos36^0+cos36^0}{sin36^0+sin36^0}.tan36^0=cot36^0.tan36^0=1\)

\(B=\frac{-\sin\left(\frac{\pi}{2}+144^0\right)-\cos126^0}{\sin144^0-\cos126^0}.\tan\left(\pi-144^0\right)\)

\(B=\frac{-\cos144^0-\cos126^0}{\sin144^0-\cos126^0}.\left(-\tan144^0\right)\)

\(B=\frac{\sin144^0.\cos144^0+\sin144^0.\cos126^0}{\sin144^0.\cos144^0-\cos144^0.\cos126^0}\)

\(B=\frac{\sin\left(\pi+\frac{\pi}{2}-126^0\right)[\cos\left(\pi+\frac{\pi}{2}-126^0\right)+\cos126^0]}{\cos\left(\pi+\frac{\pi}{2}-126^0\right)[\sin\left(\pi+\frac{\pi}{2}-126^0\right)-\cos126^0]}\)

\(\sin\left(\pi+\frac{\pi}{2}-126^0\right)=-\sin\left(\frac{\pi}{2}-126^0\right)=-\cos126^0\)

\(\cos\left(\pi+\frac{\pi}{2}-126^0\right)=-\cos\left(\frac{\pi}{2}-126^0\right)=-\sin126^0\)

\(\Rightarrow B=\frac{-\cos126^0\left(-\sin126^0+\cos126^0\right)}{-\sin126^0\left(-\cos126^0-\cos126^0\right)}\)

\(=\cot126^0.\frac{\sin126^0-\cos126^0}{2\cos126^0}\)

\(=\cot126^0\left(\frac{1}{2}.\tan126^0-\frac{1}{2}\right)\)

\(=\frac{1}{\tan126^0}.\frac{1}{2}.\tan126^0-\frac{1}{2}.\cot126^0=\frac{1}{2}\left(1-\cot126^0\right)\)

Thế này là gọn nhất rồi đấy :<

\(=\frac{cos36-sin\left(180+54\right)}{sin\left(180-36\right)-cos\left(90+36\right)}.cos54=\frac{cos36+sin54}{sin36+sin36}.cos54\)

\(=\frac{cos36+cos36}{2sin36}.sin36=cos36\)

rút gọn biểu thức:

E=cos(\(\dfrac{3\pi}{3}-\alpha\))-sin(\(\dfrac{3\pi}{2}-\alpha\))+sin(\(\alpha+4\pi\))

a) \(\dfrac{\sin2\text{a}+\cos a}{1+\cos2\text{a}+\cos a}=2\tan a\)

a) \(\dfrac{sin2\alpha+sin\alpha}{1+cos2\alpha+cos\alpha}=\dfrac{2sin\alpha cos\alpha+sin\alpha}{2cos^2\alpha+cos\alpha}\)\(=\dfrac{sin\alpha\left(2cos\alpha+1\right)}{cos\alpha\left(2cos\alpha+1\right)}=\dfrac{sin\alpha}{cos\alpha}=tan\alpha\).

a)\(sin\left(\alpha+\dfrac{\pi}{2}\right)=cos\left[\dfrac{\pi}{2}-\left(\alpha+\dfrac{\pi}{2}\right)\right]=cos\left(-\alpha\right)=cos\alpha\).
b) \(cos\left(x+\dfrac{\pi}{2}\right)=sin\left[\dfrac{\pi}{2}-\left(x+\dfrac{\pi}{2}\right)\right]=sin\left(-x\right)=-sinx\).
c) \(tan\left(\alpha+\dfrac{\pi}{2}\right)=\dfrac{sin\left(\alpha+\dfrac{\pi}{2}\right)}{cos\left(\alpha+\dfrac{\pi}{2}\right)}=\dfrac{cos\alpha}{-sin\alpha}=-cot\alpha\).
d) \(cot\left(\alpha+\dfrac{\pi}{2}\right)=\dfrac{cos\left(\alpha+\dfrac{\pi}{2}\right)}{sin\left(\alpha+\dfrac{\pi}{2}\right)}=\dfrac{-sin\alpha}{cos\alpha}=-tan\alpha\).

a)\(sin^2\left(180^o-\alpha\right)+tan^2\left(180-\alpha\right).tan^2\left(270^o+\alpha\right)\)\(+sin\left(90^o+\alpha\right)cos\left(\alpha-360^o\right)\)
\(=sin^2\alpha+tan^2\alpha.cot^2\alpha+cos\alpha cos\alpha\)
\(=sin^2\alpha+cos^2\alpha+\left(tan\alpha cot\alpha\right)^2=1+1=2\).

\(\dfrac{cos\left(\alpha-180^o\right)}{sin\left(180^o-\alpha\right)}+\dfrac{tan\left(\alpha-180^o\right)cos\left(180^o+\alpha\right)sin\left(270^o+\alpha\right)}{tan\left(270^o+\alpha\right)}\)
\(=\dfrac{cos\left(180^o-\alpha\right)}{sin\left(180^o-\alpha\right)}+\dfrac{-tan\left(180^o-\alpha\right).cos\alpha.sin\left(90^o+\alpha\right)}{-tan\left(90^o+\alpha\right)}\)
\(=tan\left(180^o-\alpha\right)+\dfrac{tan\alpha.cos\alpha.cos\alpha}{cot\alpha}\)
\(=-tan\alpha+tan^2\alpha cos^2\alpha\)
\(=tan\alpha\left(-1+tan\alpha cos^2\alpha\right)\)
\(=tan\alpha\left(sin\alpha cos\alpha-1\right)\).