а) (1-sinα)(1+sinα) = 1+sinα-sinα-sinα×sinα = 1+sinα-sinα-sin²α = 1-sin²α = cos²α
б)
в)
г) 1-cos²α+sin²α = sin²α+sin²α = 2sin²α
д) cos⁴α + sin²α×cos²α = (cos²α + sin²α)×cos²α = 1×cos²α = cos²α
е)
а) (1-sinα)(1+sinα) = 1+sinα-sinα-sinα×sinα = 1+sinα-sinα-sin²α = 1-sin²α = cos²α
б)![\frac{1}{cos^{2}\alpha}-tg^{2}\alpha = \frac{1}{cos^{2}\alpha}-\frac{sin^{2}\alpha}{cos^{2}\alpha} = \frac{1-sin^{2}\alpha}{cos^{2}\alpha} = \frac{cos^{2}\alpha}{cos^{2}\alpha} = 1](/tpl/images/1595/3438/c29ff.png)
в)![\frac{cos^{2}\alpha}{1-sin^{2}\alpha} =\frac{cos^{2}\alpha}{cos^{2}\alpha}=1](/tpl/images/1595/3438/30cb3.png)
г) 1-cos²α+sin²α = sin²α+sin²α = 2sin²α
д) cos⁴α + sin²α×cos²α = (cos²α + sin²α)×cos²α = 1×cos²α = cos²α
е)![\frac{sin\alpha}{1+cos\alpha}+\frac{1+cos\alpha}{sin\alpha} = \frac{sin^{2}\alpha+(1+cos\alpha)^{2}}{(1+cos\alpha)*sin\alpha} = \frac{sin^{2}\alpha + 1+2cos\alpha +cos^{2}\alpha}{(1+cos\alpha)*sin\alpha} = \frac{1+1+2cos\alpha}{(1+cos\alpha)*sin\alpha} = \frac{2+2cos\alpha}{(1+cos\alpha)*sin\alpha} = \frac{2(1+cos\alpha)}{(1+cos\alpha)*sin\alpha} = \frac{2}{sin\alpha} = 2csc\alpha](/tpl/images/1595/3438/0061c.png)