Question

1)cos^2(альфа)-cos^4(альфа)+sin^4(альфа) 2)1-2cos^2(бета)------------------------cos(бета)+sin(бета)3) (sin^2альфа+tg^2альфа sin^2 альфа) Ctg(альфа)4) cos^2(альфа)-1-------------------------- + tg^2(альфа)cos^4 (альфа)

Answer 1

знаю только первое,остальное без понятия

Answer 2

3)(sin^2a+sin^4a/cos^2a)*cosa/sina=sin^2a(cos^2a+sin^2a)*cosa/(sina*cos^2a)=(sina/cosa)

4)(cosa-1)(cosa+1)/cos^4a+sin^2a/cos^2a=(cos^2a-1+sin^2a*cos^2a)/cos^4a=(sin^2a*cos^2a-sin^2a)/cos^4a=sin^2a(cos^2a-1)/cos^4a=tg^2a(cos^2a-1)/cos^2a

Answer 3

Let's simplify each of the expressions step by step:

1. cos^2(α) - cos^4(α) + sin^4(α):

First, let's factor out a common term, which is cos^2(α): cos^2(α) (1 - cos^2(α) + sin^2(α))

Now, you can use the trigonometric identity sin^2(α) + cos^2(α) = 1: cos^2(α) (1 - cos^2(α) + (1 - cos^2(α)))

Now, simplify further: cos^2(α) (2 - 2cos^2(α))

2cos^2(α) - 2cos^4(α)

2. 1 - 2cos^2(β) / (cos(β) + sin(β)):

You can factor out a common term in the denominator, which is 1: (1 - 2cos^2(β)) / (1/cos(β) + sin(β)/cos(β))

Now, you can simplify further by combining the fractions in the denominator: (1 - 2cos^2(β)) / (cos(β) + tan(β))

3. (sin^2(α) + tan^2(α) sin^2(α)) * Ctg(α):

First, expand the expression: (sin^2(α) + sin^2(α)tan^2(α)) * Ctg(α)

Now, factor out sin^2(α) from the first two terms: sin^2(α) (1 + tan^2(α)) * Ctg(α)

Now, use the trigonometric identity 1 + tan^2(α) = sec^2(α): sin^2(α) * sec^2(α) * Ctg(α)

Now, simplify by using the identity Ctg(α) = 1/tan(α): sin^2(α) * sec^2(α) / tan(α)

4. cos^2(α) - 1 / (1 + tg^2(α)cos^4(α)):

First, factor out a common term in the denominator, which is 1: (cos^2(α) - 1) / (1 + tg^2(α)cos^4(α))

Now, use the identity cos^2(α) - sin^2(α) = 1: (-sin^2(α)) / (1 + tg^2(α)cos^4(α))

Please note that these simplified expressions are in terms of trigonometric functions, and they may not have a simpler algebraic form.