Question

1.Решите уравнение: (sinx+1/2)(cosx-1)=0 2.Упростите ворожение: 1-cos^2x c подробным решением !

Answer 1

1
(sinx+1/2)(cosx-1)=0
[sinx+1/2=0⇒sinx=-1/2⇒x=(-1)^(n+1)*π/6+πn,n∈z
[cosx-1=0⇒cosx=1⇒x=2πn,n∈z
2
1-cos²x=sin²x+cos²x-cos²x=sin²x

Answer 2

1. Решение уравнения: (sinx + 1/2)(cosx - 1) = 0

To solve the equation (sinx + 1/2)(cosx - 1) = 0, we need to find the values of x that make the equation true.

To do this, we can set each factor equal to zero and solve for x:

sinx + 1/2 = 0 (Equation 1) cosx - 1 = 0 (Equation 2)

Let's solve Equation 1 first:

sinx + 1/2 = 0

Subtracting 1/2 from both sides:

sinx = -1/2

The solutions to this equation can be found by looking at the unit circle or using trigonometric identities. The angles that satisfy sinx = -1/2 are x = 7π/6 + 2πn and x = 11π/6 + 2πn, where n is an integer.

Now let's solve Equation 2:

cosx - 1 = 0

Adding 1 to both sides:

cosx = 1

The solutions to this equation can be found by looking at the unit circle or using trigonometric identities. The angle that satisfies cosx = 1 is x = 2πn, where n is an integer.

Therefore, the solutions to the equation (sinx + 1/2)(cosx - 1) = 0 are x = 7π/6 + 2πn, x = 11π/6 + 2πn, and x = 2πn, where n is an integer. [[1]]

2. Упрощение выражения: 1 - cos^2x + c

To simplify the expression 1 - cos^2x + c, we can use trigonometric identities.

The identity we can use here is the Pythagorean identity: sin^2x + cos^2x = 1.

Let's rewrite the expression using this identity:

1 - cos^2x + c = sin^2x + c

Now, the expression is simplified to sin^2x + c.

Please note that without a specific value for c, we cannot simplify the expression further. The value of c will determine the final form of the simplified expression.