Question

Обчислити sinx(3-4sin^2x)/cosx(4cos^2x-3), якщо ctgx=5/3.

Answer 1

сtgx=5/3
sin²x=1:(1+ctg²x)=1:(1+25/9)=9/34
sinx=3/√34
cos²x=1-sin²x=1-9/34=25/34
cosx=5/√34
sinx(3-4sin²x)/cosx(4cos²x-3)=3/√34*(3-18/17):5√34*(50/17-3)=
=3/√34*33/17:5/√34*(-1/17)=-99/17√34*17√34=-99