Question

(Cosальфа-sinальфа)(cosальфа+sinальфа)/cos2альфа

Answer 1

Ответ:

..................

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Answer 2

Ответ:

(Cos(x) - Sin(x))(Cos(x)+Sin(x))/Cos(2x) =

= (Cos(x)^2 - Sin(x)^2)/Cos(2x) =

= Cos(2x)/Cos(2x) = 1

примечание : Cos(2x) = Cos(x)^2 - Sin(x)^2

Answer 3

To simplify the given expression, we'll use the trigonometric identities:

1. $\cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$
2. $\cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$
3. $\sin^2 \alpha + \cos^2 \alpha = 1$

Let's proceed with the simplification:

1. First, we'll rewrite the expression using the trigonometric identities: $(\cos \alpha - \sin \alpha)(\cos \alpha + \sin \alpha) = \cos^2 \alpha - \sin^2 \alpha$

2. Now, we can use the identity $\cos^2 \alpha - \sin^2 \alpha = \cos(2\alpha)$: $(\cos \alpha - \sin \alpha)(\cos \alpha + \sin \alpha) = \cos(2\alpha)$

3. Finally, we divide the expression by $\cos^2 \alpha$: $\frac{\cos(2\alpha)}{\cos^2 \alpha}$

So, the simplified form of the expression is $\frac{\cos(2\alpha)}{\cos^2 \alpha}$.