To solve this equation, we can use the zero product property which states that if a product of factors is equal to zero, then at least one of the factors must be zero.
Given: (5cosx-3√3)(5cosx-2√6)=0
To find the values of x that make the equation true, we set each factor to zero and solve for x separately.
1) 5cosx - 3√3 = 0 5cosx = 3√3 cosx = 3√3 / 5
Using a calculator, we find that cosx ≈ 0.7746. Taking the inverse cosine of 0.7746 gives x ≈ 0.7314.
2) 5cosx - 2√6 = 0 5cosx = 2√6 cosx = 2√6 / 5
Using a calculator, we find that cosx ≈ 0.8944. Taking the inverse cosine of 0.8944 gives x ≈ 0.4628.
Therefore, the solutions to the equation (5cosx-3√3)(5cosx-2√6)=0 are x ≈ 0.7314 and x ≈ 0.4628.
To solve this equation, we can use the zero product property which states that if a product of factors is equal to zero, then at least one of the factors must be zero.
Given:
(5cosx-3√3)(5cosx-2√6)=0
To find the values of x that make the equation true, we set each factor to zero and solve for x separately.
1) 5cosx - 3√3 = 0
5cosx = 3√3
cosx = 3√3 / 5
Using a calculator, we find that cosx ≈ 0.7746. Taking the inverse cosine of 0.7746 gives x ≈ 0.7314.
2) 5cosx - 2√6 = 0
5cosx = 2√6
cosx = 2√6 / 5
Using a calculator, we find that cosx ≈ 0.8944. Taking the inverse cosine of 0.8944 gives x ≈ 0.4628.
Therefore, the solutions to the equation (5cosx-3√3)(5cosx-2√6)=0 are x ≈ 0.7314 and x ≈ 0.4628.