pake cara ya nomor 4 aja

[tex]\frac1{\sec\alpha-\tan\alpha}-\frac1{\sec\alpha+\tan\alpha}[/tex]
kita samakan penyebutnya dahulu
[tex]=\frac{{\sec\alpha+\tan\alpha}-{(\sec\alpha-\tan\alpha)}}{\sec^2\alpha-\tan^2\alpha}[/tex]
[tex]=\frac{{\sec\alpha+\tan\alpha}{-\sec\alpha+\tan\alpha}}{\sec^2\alpha-\tan^2\alpha}[/tex]
[tex]=\frac{{2\tan\alpha}}{\sec^2\alpha-\tan^2\alpha}[/tex]
[tex]=\frac{{2\tan\alpha}}{\frac1{\cos^2\alpha}-\frac{sin^2\alpha}{cos^2\alpha}}[/tex]
[tex]=\frac{{2\tan\alpha}}{\frac{1-sin^2\alpha}{cos^2\alpha}}[/tex]
[tex]=\frac{{2\tan\alpha}}{\frac{sin^2\alpha+cos^2\alpha-sin^2\alpha}{cos^2\alpha}}[/tex]
[tex]=\frac{{2\tan\alpha}}{\frac{cos^2\alpha}{cos^2\alpha}}[/tex]
[tex]=\frac{2\tan\alpha}1[/tex]
[tex]=2\tan\alpha[/tex]
terbukti

semoga membantu, mohon dikoreksi bila ada kesalahan