Question

1) ctg^2 b(бета)*(cos^2 b-1)+1=

Answer 1

Ctg^2b*sin^2b+1=cos^2b/sin^2b * sin^2b +1= cos^2b+1

Answer 2

The equation you provided seems to be a mathematical expression involving trigonometric functions, specifically cotangent (ctg) and cosine (cos). Let me break down the expression for you and simplify it as much as possible.

The given expression is:

$\text{ctg}^2(\beta) \times (\cos^2(\beta) - 1) + 1$

To simplify this expression, we can use trigonometric identities:

1. $\text{ctg}^2(\beta) = 1/\tan^2(\beta)$
2. $\cos^2(\beta) - 1 = -\sin^2(\beta)$

Using these identities, the expression can be rewritten as:

$\frac{1}{\tan^2(\beta)} \times (-\sin^2(\beta)) + 1$

Further simplifying, we get:

$-\frac{\sin^2(\beta)}{\tan^2(\beta)} + 1$

Recall that $\tan(\beta) = \frac{\sin(\beta)}{\cos(\beta)}$. Substituting this into the expression, we get:

$-\frac{\sin^2(\beta)}{\left(\frac{\sin(\beta)}{\cos(\beta)}\right)^2} + 1$

Simplifying the expression inside the parentheses, we have:

$-\frac{\sin^2(\beta) \times \cos^2(\beta)}{\sin^2(\beta)} + 1$

Canceling out $\sin^2(\beta)$, we get:

$-\cos^2(\beta) + 1$

Finally, the simplified expression is:

$1 - \cos^2(\beta)$

This expression represents a well-known trigonometric identity, which is the square of the sine function:

$1 - \cos^2(\beta) = \sin^2(\beta)$