$\frac{(\sec \theta-\tan \theta)}{(\sec \theta+\tan \theta)}=\left(1+2 \tan ^{2} \theta-2 \sec \theta \tan \theta\right)$
$\frac{\sec \theta-\tan \theta}{\sec \theta+\tan \theta}$
$=\frac{\sec \theta-\tan \theta}{\sec \theta+\tan \theta} \times \frac{\sec \theta-\tan \theta}{\sec \theta-\tan \theta}$
$=\frac{(\sec \theta-\tan \theta)^{2}}{(\sec \theta+\tan \theta)(\sec \theta-\tan \theta)}$
$=\frac{\sec ^{2} \theta+\tan ^{2} \theta-2 \sec \theta \tan \theta}{\sec ^{2} \theta-\tan ^{2} \theta} \quad\left[(a-b)^{2}=a^{2}+b^{2}-2 a b\right.$ and $\left.(a+b)(a-b)=a^{2}-b^{2}\right]$
$=\frac{1+\tan ^{2} \theta+\tan ^{2} \theta-2 \sec \theta \tan \theta}{1} \quad\left(1+\tan ^{2} \theta=\sec ^{2} \theta\right)$
$=1+2 \tan ^{2} \theta-2 \sec \theta \tan \theta$
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