Question

√3cos(π/2-x)-1,5=0 cos²x+sin(π/2+x)+sin²x=1 3tg π/6 cos (x+π/3)-√3=0 Решите пожалуйста!!! Срочно

Answer 1

1
√3sinx=3/2
sinx=√3/2
x=(-1)^n*π/3+πn,n∈z
2
1+cosx=1
cosx=0
x=π/2+πn,n∈z
3
3*√3/3*cos(x+π/3)=√3
cos(x+π/3)=1
x+π/3=2πn
x=-π/3+2πn,n∈z

Answer 2

Equation 1: √3cos(π/2-x)-1.5=0

To solve this equation, we can isolate the cosine term and then solve for x. Here's the step-by-step solution:

1. Add 1.5 to both sides of the equation: √3cos(π/2-x) = 1.5

2. Divide both sides of the equation by √3: cos(π/2-x) = 1.5/√3

3. Take the inverse cosine (arccos) of both sides to solve for x: π/2 - x = arccos(1.5/√3)

4. Subtract arccos(1.5/√3) from π/2 to solve for x: x = π/2 - arccos(1.5/√3)

Let's calculate the value of x using the given equation:

x = π/2 - arccos(1.5/√3) ≈ 0.5236 radians or approximately 30 degrees.

Equation 2: cos²x+sin(π/2+x)+sin²x=1+3tg(π/6)+cos(x+π/3)-√3=0

To solve this equation, we can simplify it step by step:

1. Simplify the trigonometric terms: cos²x + sin(π/2+x) + sin²x = 1 + 3tan(π/6) + cos(x+π/3) - √3 = 0

2. Use trigonometric identities to simplify further: cos²x + cos(x) + sin²x = 1 + √3/3 + cos(x) - √3 = 0

3. Combine like terms: 2cos(x) + 2sin²x = 1 + √3/3

4. Use the identity sin²x = 1 - cos²x: 2cos(x) + 2(1 - cos²x) = 1 + √3/3

5. Simplify the equation: 2cos(x) + 2 - 2cos²x = 1 + √3/3

6. Rearrange the equation: 2cos²x - 2cos(x) + (1 + √3/3 - 1) = 0

7. Combine like terms: 2cos²x - 2cos(x) + √