Cos2x formula in terms of sin :
- cos2x = 1–2sin2x
- cos2x = cos2x-sin2x
Cos2x formula in terms of cos :
- cos2x = cos2x-sin2x
- cos2x = 2cos2x-1
Cos2x formula in terms of tan :
- cos2x =1 — tan2x / 1 + tan2x
Graph of Cos2x
The integral of cos2x = (1/2)sin(2x) + C, Where C is constant.
Finding the integral of Cos(2x)
f(x) = cos(x)
g(x) = 2x
f(g(x))= cos(2x)
Let u = g(x) =2x
then du = g’(x) = 2dx, and d(x) = (1/2)du
Plug in u for 2x and (1/2)du for dx.
∫Cos(2x)dx = ∫(1/2)cos(u)du
Now we want to find ∫(1/2)cos(u)du
∫(1/2)cos(u)du = (1/2)∫cos(u) = (1/2)sin(u)+c ___(1)
Then Subtitute Value of u in (1) we get….
∫(1/2)cos(2x)du = (1/2)sin(2x)+c
The integral of cos2x = (1/2)sin(2x) + C, Where C is constant.
