Sin(x+60)°=cos(2x),find tan (x+60)°

Answer 1

To find tan(x+60)°, we can use the identities:

sin(x+60) = cos(90 - (x+60)) = cos(30-x)

Therefore, cos(30-x) = cos(2x)

Since cos is an even function, cos(a) = cos(-a). So, we can rewrite the equation as:

cos(x-30) = cos(2x)

Equating the arguments:

x - 30 = 2x

x = -30

Now, we can find tan(x+60)°:

tan(-30+60)° = tan(30)° = sin(30) / cos(30) = (1/2) / (sqrt(3)/2) = 1 / sqrt(3) = sqrt(3) / 3

Therefore, tan(x+60)° = sqrt(3) / 3