Verify the identity: sec(4x)=1/(√(2)sin(x)cos(x)-1)-1/(√(2)sin(x)cos(x)+1)

Answer 1

Great analysis. Much shorter than my first attempt.....

Answer 2

Based on the equation you wrote: they are NOT equal statements.

For example, consider when x = 0.

sec(4 * 0) = sec(0) = 1

BUT, 1/sqrt(2sin(0)cos(0) - 1) (the first term on the right side of the equation) yields 1/sqrt(-1), which is an imaginary number. Although the second term yields the number 1 (because 1/sqrt(2sin(0)cos(0) + 1) = 1, but the first term makes it a complex number, and cannot equal 0. So, unless if that equation was not really the equation you wanted me to figure out (I reread it numerous times just to make sure), then that identity is FALSE.