Question

is 2cosx*sinx the same thing as 2sinx*cosx?

Answer 1

Yes, 2 (cosx)×(sinx) =2(sinx)×(cosx) are the same thing or having same value.

Let us see how

Trignometric functions are scaler quantity .It means in trigonometric functions while solving questions direction does not matter.

Like 2×(x)×(y) =2×(y)×(x) =2xy or 2yx

Similarly for trignometric functions.

2(cosx)(sinx) =2(sinx)(cosx) = sin(2x)

Example At x =30°

sin30° = 0.5

cos 30° = 0.866

Now, 2×(sin30°)×(cos30°) = 2×0.5×0.866=0.866 ..........1

And 2×(cos30°)×(sin30°) = 2+×8.66×0.5 =0.866 ..........2

Again from both the equations we can say,

2×(sinx)×(cosx) = 2×(cosx)×(sinx).