(1)因为log(3)5=a,5的b次 =7即:log(3)5=a,log(5)7=b,log(3)7=a/b
所以log(63)105=log(63)3x7x5=log(63)3+log(63)7+log(63)5=1/log(3)63+1/log(7)63+1/log(5)63=(a+b)/(a+2b)+a/(ab+2)
(2)(lg2)^2+lg5*lg20-1=(lg2)^2+lg5x(lg2+lg10)-1=(lg2)^2+lg5xlg2+lg5-1=lg2(lg2+lg5)+lg5-1=lg2+lg5-1=0
(3)【(secA-cosA)(cscA-sinA)】/【2sinA-cosA】=(1/cosA-cosA)(1/sinA-sinA)/(2sinA-cosA)
=(1/sinacosa-sina/coa-cosa/sina+sinacosa)/(2sinA-cosA)
=[(sina)^2+(cosA)^2]sinacosa-sina/coa-cosa/sina+sinacosa)/(2sinA-cosA)
=(sinacosa)/(2sinA-cosA)