Question

2) cos²x – 3sinxcosx -1;

Answer 1

Ответ: cos^2x-3sinxcosx=-1

cos^2x-3sincos+sin^2+cos^2=0

2cos^2+sin^2-3sincos=0

2+tg^2-3tg=0

D=1

X1,2 = 2; 1

tgx=2 tgx=1

x=arctg2+pk x=p/4+pk

x=p-arctg2+pk

Answer 2

To simplify the expression $\cos^2(x) - 3\sin(x)\cos(x) - 1$, you can use trigonometric identities and algebraic manipulation. Here's how you can do it:

1. Start with the expression: $\cos^2(x) - 3\sin(x)\cos(x) - 1$

2. Use the Pythagorean trigonometric identity $\sin^2(x) + \cos^2(x) = 1$ to express $\cos^2(x)$ in terms of $\sin(x)$: $1 - \sin^2(x) - 3\sin(x)\cos(x) - 1$

3. Notice that the "1" terms on both sides of the equation cancel out: $-\sin^2(x) - 3\sin(x)\cos(x)$

4. Factor out a common factor of $-\sin(x)$ from the remaining terms: $-\sin(x)(\sin(x) + 3\cos(x))$

So, the simplified expression is $-\sin(x)(\sin(x) + 3\cos(x))$.