Question

函数f(x)=sinx/根号（1+cos²x),它的最小正周期是?

Answer 1

f(x)=sinx/√[sin^2(x)+cos^2(x)+con^2(x)]

=sinx/√[sin^2(x)+2cos^2(x)]

=1/{√[sin^2(x)+2cos^2(x)]/sin^2(x)}

=1/√[1+2tan^2(x)]

tanx的最小正周期是∏,则f(x)的最小正周期也是∏