Cos ( 27/2 - x )=√ 3/2

Предыдущий
вопрос Следующий
вопрос

To solve this equation, we need to use the definition of cosine.

We know that cos(30 degrees) = sqrt(3)/2.

Since 27/2 is very close to 30, we can rewrite the equation as:

cos(30 - x) = sqrt(3)/2

We also know that cos(30 - x) = cos(30)cos(x) + sin(30)sin(x) by the cosine of a difference formula.

Therefore, we have:

(sqrt(3)/2) = (sqrt(3)/2)cos(x) + (1/2)sin(x)

Multiplying through by 2 to clear the fractions gives us:

sqrt(3) = sqrt(3)cos(x) + sin(x)

Now, we know that sin(30 degrees) = 1/2 and cos(30 degrees) = sqrt(3)/2.

Therefore, sin(x) = sin(30)cos(x) + cos(30)sin(x)

sin(x) = (1/2)cos(x) + (sqrt(3)/2)sin(x)

Multiplying through by 2 gives:

2sin(x) = cos(x) + sqrt(3)sin(x)

Rearranging terms:

2sin(x) - sqrt(3)sin(x) = cos(x)

sin(x) = cos(x)

This implies that x is equal to 45 degrees because at 45 degrees, sin(45) = sqrt(2)/2 and cos(45) = sqrt(2)/2.

Therefore, the solution to the equation is x = 45 degrees.