F(x) = sec x. Let x and 2x be in Dom f. Determine whether the following statement is true or false:?

f(2x) = ((f(x))^2)/(2-(f(x))^2)F(x) = sec x. Let x and 2x be in Dom f. Determine whether the following statement is true or false:?
You want to know if





sec 2x = [ sec^2 x ] / [ 2 - sec^2 x ]





So let's work backwards. Start by taking the reciprocal of both sides:





1 / sec 2x ? [ 2 - sec^2 x ] / [sec^2 x]





Since secant is the reciprocal of cosine:





cos 2x ? cos^2 x [ 2 - sec^2 x ]





Multiply through by cos^2 x on the RHS:





cos 2x ? 2 cos^2 x - cos^2 x * sec^2 x


cos 2x ? 2 cos^2 x - 1.





So, does equality hold on the last line?





Good luck.