Question

Упростите выражение (1-sinx)/cosx

Answer 1

(sin²x/2+cos²x/2-2sinx/2cosx/2)/(cos²x/2-sin²x/2)=
=(cosx/2-sinx/2)²/(cosx/2-sinx/2)(cosx/2+sinx/2)=(cosx/2-sinx/2)/(cosx/2+sinx/2)=
=√2(1/√2cosx/2-1/√2sinx/2)/√2(1/√2cosx/2+1/√2sinx/2)=cos(x/2+π/4)/sin(π/4+x/2)=
=ctg(x/2+π/4) или tg(x/2-π/4)