Question

H. Find the range of the function f(x) = cos 2x, when x E R.​

Answer 1

Answer:

f(x)cosx−cos2x

⇒ we know domain of f(x)willbe−∞<x<∞ and period of cosx=2π 

Now f(x)=cosx−cos2x

=f1(x)=−sinx+2cosxsinx

For eritical pointf1(x)=0

−sinx+2cosxsinx=0

sinx(2cosx−1)=0

2cosx−1=0sinx=0

cosx=21x=nπ(nϵz)

x=3π+3nπor3−π+2nπ(nϵz)

Now f1(x)=sinx+sin2x

f11(x)=−cosx+2cos2x

f11(nπ)=−cos(nπ)+2cos(2nπ)