Question

Como se desarrolla esta identidad Sec4 x - tan4 x = 2 sec2 x -1

Answer 1

${sec^4x-tan^4x=}\\\\{sec^4x-\frac{sen^4x}{cos^4x}=}\\\\{ \frac{cos^4x.sec^4x-sen^4x}{cos^4x} =}\\\\{ \frac{1-sen^4x}{cos^4x} =}\\\\{ \frac{(1-sen^2x)(1+sen^2x)}{cos^2x.cos^2x} =}\\\\{ \frac{(cos^2x)(1+1-cos^2x)}{cos^2x.cos^2x} =}\\\\{ \frac{2-cos^2x}{cos^2x} =}\\\\{ \frac{2}{cos^2x} - \frac{cos^2x}{cos^2x} =}\\\\{\boxed{2sec^2x-1}}\\\\{\text{salu2.!! :)}}$