2. Упростить: (cos2(п/2 + x) – 1)/sin2(п + x)

Question

2. Упростить: (cos2(п/2 + x) – 1)/sin2(п + x)

Answer 1

(cos2(п/2 + x) – 1)/sin2(п + x) = (cos(п + 2x) – 1)/sin(2п +2 x) = (-cos(2x) - 1)/sin2x = 

= {-[cos^2(x) - sin^2(x)] - [cos^2(x) + sin^2(x)]}/(2sinxcosx) = 

= [-2cos^2(x)]/(2sinxcosx) = -cosx/sinx = -ctgx