Question

Cos(pi/2+x)=cos pi/6

Answer 1

Левую часть преобразуем по формулам приведения:

-sinx=V3/2; sinx=-V3/2; x=(-1)^n*4пи/3+пиn, n---Z.

Answer 2

To solve the equation cos(pi/2 + x) = cos(pi/6), we can use the trigonometric identity:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

In this case, A = pi/2 and B = x. Substituting these values into the identity, we have:

cos(pi/2 + x) = cos(pi/2)cos(x) - sin(pi/2)sin(x)

Since cos(pi/2) = 0 and sin(pi/2) = 1, we can simplify the equation further:

0cos(x) - 1sin(x) = cos(pi/6)

-sin(x) = cos(pi/6)

Now, we can use another trigonometric identity:

cos(pi/6) = sqrt(3)/2 sin(pi/6) = 1/2

Substituting these values into the equation, we get:

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

To solve for x, we take the inverse sine (or arcsin) of both sides:

sin^(-1)(-sin(x)) = sin^(-1)(sqrt(3)/2)

x = -pi/3 + 2pin or x = pi - pi/3 + 2pin

where n is an integer.

So the solutions for x are:

x = -pi/3 + 2pin or x = 2pi/3 + 2pin

where n is an integer.