`a)`
`A=2cot37^o . cot53^o + sin^2 28^o - (3tan54^o)/(cot36^o)+sin^2 62^o`
`A=2cot37^o . cot(90^o-37^o) + sin^2 28^o –(3tan54^o)/(cot(90^o-54^o))+ sin^2 (90^o-28^o)`
`A=2cot37^o . tan37^o+sin^2 28^o-(3tan54^o)/(tan54^o)+cos^2 28^o`
`A=2+sin^2 28^o-3+cos^2 28^o=-1+1=0`
`b)`
Ta có: `sin^2 alpha+cos^2 alpha=1`
`<=> cos^2 alpha=1-sin^2 alpha`
`=> cos^2 alpha=1-(1/(sqrt3))^2=1-1/3=2/3`
`=> cos alpha=+-(sqrt6)/3`
Lại có: `1+tan^2 alpha=1/(cos^2 alpha)`
`<=> 1+tan^2 alpha=1:2/3=3/2`
`<=> tan^2alpha=3/2-1=1/2`
`<=> tan alpha=+-(sqrt2)/2`
Lại có : `cot alpha=1/(tan alpha)=1 : +-(sqrt2)/2=+-sqrt2`
Vậy $\begin{cases}cos \ \alpha=\pm \dfrac{\sqrt{6}}{3}\\tan \ \alpha=\pm \dfrac{\sqrt{2}}{2}\\cot \ \alpha=\pm \sqrt{2}\end{cases}$
