已知α为锐角,且有2tan(π-α)-3cos(π2+β)+5=0,tan(π+α)+6sin(π+β)-1=0,则sinα的值是_.

问题描述:

已知α为锐角,且有2tan(π-α)-3cos(

π
2
+β)+5=0,tan(π+α)+6sin(π+β)-1=0,则sinα的值是______.

α为锐角,且有2tan(π-α)-3cos(π2+β)+5=0,可得-2tanα+3sinβ+5=0,即2tanα-3sinβ-5=0…①由tan(π+α)+6sin(π+β)-1=0,可得:tanα-6sinβ-1=0…②,①×2-②得:3tanα-9=0,∴tanα=3.tanα=si...