Question

1-tan^4x/1-tan^2x = 2-sec^x​

Answer 1

Answer:

1-tan^4(x)/sec^2(x)=1-tan^2(x) , you need to use the difference of two squares method.

Working with the left side of the equation:

1-tan4(x) = ( 1- tan2(x)) (1 + tan2(x)) then you have ( 1- tan2(x)) (1 + tan2(x)) / sec2(x)

but sec2(x) = ( 1 + tan2(x)) ( Trigonometric identities )

Then the expression becomes ( 1- tan2(x)) (sec2(x)) / sec2(x) , and sec2(x) cancels out from both

the numerator and the denominator and you are left with ( 1- tan2(x)) , which is what you have on the right side of the equation.