Помогите с тригонометрией Пример во вложении

1) sin^2 (3pi/2 - a) = (-cos a)^2 = cos^2 a tg^2 a - 1 = sin^2 a / cos^2 a - 1 = (sin^2 a - cos^2 a)/cos^2 a = = -cos 2a / cos^2 a ctg(a - 5pi/4) = cos(a - 5pi/4) / sin(a - 5pi/4) [latex]sin(\frac{5pi}{4} + a) = sin( \frac{5pi}{2}-\frac{5pi}{4}+ a) = sin(2pi + \frac{pi}{2}-\frac{5pi}{4} + a) = [/latex] [latex]= sin( \frac{pi}{2}-\frac{5pi}{4} + a) = cos(\frac{5pi}{4} - a) = cos(a - \frac{5pi}{4})[/latex] [latex]sin^{-2}(\frac{5pi}{4}+a)= \frac{1}{cos^2(a-5pi/4)} [/latex] Подставляем все это [latex]cos^2(a)* \frac{-cos(2a)}{cos^2(a)} * \frac{cos(a - 5pi/4)}{sin(a - 5pi/4)}* \frac{1}{cos^2(a - 5pi/4)} = [/latex] [latex]=- \frac{cos(2a)}{sin(a - 5pi/4)cos(a - 5pi/4)} =- \frac{cos(2a)}{1/2*sin(2a-5pi/2)} =- \frac{2cos(2a)}{cos(2a)} =-2[/latex]