三角函数 (2 21:19:19)
2个回答

f(x)+f(60°-x)

=cosx/cos(30-x)+cos(60-x)/cos[30-(60-x)]

=cosx/cos(30-x)+cos(60-x)/cos[x-30]

=[cosx+cos(60-x)]/cos(30-x)

=[cosx+cos60*cosx+sin60*sinx]/(cos30*cosx+sin30*sinx)

=[(3/2)cosx+(√3/2)sinx]/[(√3/2)cosx+(1/2)sinx]

=√3

f(1°)+f(2°)+.+f(59°)

=f(1°)+f(59°)+f(2°)+f(58°)+.+f(29°)+f(31°)+2f(30°)-f(30°)

=30*√3-√3/2

=30√3-√3/2

=59√3/2