Упростить: cos a + ctg a / ctg a - sin a - 1 sin^2 a + cos (п/3 - а) * cos (п/3+а)

[latex]cosa + \frac{cta}{cta} - sina - 1 = cosa + 1 - sina - 1 = cosa - sina[/latex] sin²a + cos([latex] \frac{ \pi }{3} [/latex]+a)*cos([latex] \frac{ \pi }{3} [/latex]-a) = sin²a + 1/2 * (cos([latex] \frac{ \pi }{3} [/latex]+a+[latex] \frac{ \pi }{3} [/latex]-a) + cos([latex] \frac{ \pi }{3} [/latex]+a-[latex] \frac{ \pi }{3} [/latex]+a)) = sin²a + 1/2 * (cos[latex] \frac{2 \pi }{3} [/latex] + cos2a) = [latex] \frac{2sin^2a+cos \frac{2 \pi }{3} + 1 - 2sin^2a }{2} = \frac{cos \frac{2\pi }{3} + 1}{2} = cos^2 \frac{ \pi}{3} = \frac{1}{4} [/latex]