1) 1–$si{n}^2\alpha —co{s}^2\alpha$ = 1 - sin²α + cos²α = cos²α

2) ctg²a × $co{s}^2\alpha —1$ + 1 = ctg²a × cos²α - ctg²a + 1

3) 1–sin²α × cos²α × tgα / $cos\alpha —1$ = $1-si{n}^2\alpha \times co{s}^2\alpha \times tg\alpha$ / $cos\alpha —1$

4) ctgα– / sinα = 1/sinα - sin²α/sinα = 1 - sinα

5) ————— + tgα × ctgα = $1—co{s}^2\alpha$ / $1—co{s}^2\alpha$ + tgα × ctgα = 1 + tgα × ctgα

6) ctg²α — $—————1$ = ctg²α - $1—si{n}^2\alpha$ / $si{n}^2\alpha$ = ctg²α -1/sin²α

7) cos²α — $ct{g}^2\alpha +1$ × sin²α = cos²α - $ct{g}^{2}a+1$ × sin²α

8) $sin\alpha +cos\alpha$² — 2sinα × cosα / $si{n}^2\alpha —co{s}^2\alpha$ = sin²α + cos²α + 2sinα × cosα - 2sinα × cosα / $si{n}^2\alpha —co{s}^2\alpha$ = 1

9)————————— + cosα / $sin\alpha +cos\alpha$ = $1—si{n}^2\alpha$ / $sin\alpha +cos\alpha$ + cosα

10)—————— — 1 / $1—sin\alpha$ = $1—si{n}^2\alpha$ / $1—sin\alpha$ — 1