Докажите тригонометрическое тождество, ОЧЕНЬ СРОЧНО!!!

Ответ
1) 2sin^2α * cos^2α + cos^4α + sin^4α=1
***{ 2ab + b^2 + a^2 = a^2 + 2ab + b^2 = (a+b)^2 } ***
(sin α)^4 + 2*(sin α)^2 * (cos α)^2 + (cos α)^4 = 1
[(sin α)^2 + (cos α)^2]^2 = 1
1 = 1

2) 4 + (ctgα - tgα)^2 = (ctgα + tgα)^2
(ctgα + tgα)^2 - (ctgα - tgα)^2 = 4
*** {a^2 - b^2 = (a+b)(a-b)} ***
[(ctgα + tgα) + (ctgα - tgα)] * [(ctgα + tgα) - (ctgα - tgα)] = 4
2ctgα * 2tgα = 4
4* (1/tgα)*tgα = 4
tgα/tgα = 4/4
1 = 1

3) cosα *cosß*(tgα - tgß) = sin(α - ß)
cosα *cosß * [sin(α - ß) /cosα *cosß] = sin(α - ß)
sin(α - ß) = sin(α - ß)

4) (sinα/2 + cosα/2)^2 / sinα + 1 = 1
(sinα/2 + cosα/2)^2 = sinα + 1
(sinα/2 + cosα/2)^2 = 2sinα/2 * cosα/2 + 1
(sinα/2)^2 + 2sinα/2 * cosα/2 + (cosα/2)^2 = 2sinα/2 * cosα/2 + 1
(sinα/2)^2 + (cosα/2)^2 = 1
1 = 1