What does it mean when it says equivalent form of the equation?

Idon’t understand this.. will someone ? will mark brainliest along with 20 points.

Evaluate cos2θ for cosθ = square root of 3/2

White shapes and black shapes are used in a game. some of the shapes are circles. while the rest are squares. the ratio of the number of white shapes to the number of black shapes is 5: 11. the ratio of the number of white cicrles to the number of white squares is 3: 7. the ratio of the number of black circles to the number of black squres is 3: 8. work out what fraction of all the shapes are circles.