Question

(sin2 альфа + tg2 альфа* sin2 альфа)*ctg2 альфа

Answer 1

Просто подставь и все

Answer 2

To simplify the expression $(\sin^2\alpha + \tan^2\alpha \sin^2\alpha)\cot^2\alpha$, you can use trigonometric identities.

1. Start with the expression: $(\sin^2\alpha + \tan^2\alpha \sin^2\alpha)\cot^2\alpha$

2. Factor out the common factor of $\sin^2\alpha$ from the first two terms: $\sin^2\alpha(1 + \tan^2\alpha)\cot^2\alpha$

3. Use the identity $\tan^2\alpha = \sec^2\alpha - 1$: $\sin^2\alpha(1 + (\sec^2\alpha - 1))\cot^2\alpha$

4. Simplify further: $\sin^2\alpha(\sec^2\alpha)\cot^2\alpha$

5. Use the identity $\sec^2\alpha = \frac{1}{\cos^2\alpha}$: $\sin^2\alpha\left(\frac{1}{\cos^2\alpha}\right)\cot^2\alpha$

6. Combine the fractions: $\frac{\sin^2\alpha}{\cos^2\alpha}\cot^2\alpha$

7. Use the identity $\cot^2\alpha = \frac{1}{\tan^2\alpha}$: $\frac{\sin^2\alpha}{\cos^2\alpha}\cdot\frac{1}{\tan^2\alpha}$

8. Simplify the expression further: $\frac{\sin^2\alpha}{\cos^2\alpha\tan^2\alpha}$

So, the simplified expression is $\frac{\sin^2\alpha}{\cos^2\alpha\tan^2\alpha}$.