Question

Find the value of 6 – 6 sin2θ.​

Answer 1

Answer:

We may construct two cases, depending on whether  x>0, or x<0  ( Obviously  x≠0 )

Case 1:

x>0  

By applying the  AM−GM  inequality, we get:

x+1/x>=2  

With equality holding for the case,  x=1/x=1  

So,  x−1/x=0 , for  x>0  

Case 2:

x<0  

If  x<0 , then so is  1/x .

But, if both are less than  0 , then their sum must also be less than 0 , and hence cannot be  2 .

So, this case is void.

Hence, we get:

x−1/x=0 , for all real x satisfying  x+1/x=2