Chapter 7 - Chapter Test - Page 554: 6

$sec^{2}(x)tan^{2}(x) + sec^{2}(x) = sec^{4}(x)$ $sec^{2}(x) (tan^{2}(x) + 1)$ = $sec^{4}(x)$ $sec^{2}(x)$$sec^{2}(x)$ = $sec^{4}(x)$ $sec^{4}(x) = sec^{4}(x)$

Note: $tan^{2}(x) + 1 = sec^{2}(x)$ $sec^{2}(x)tan^{2}(x) + sec^{2}(x) = sec^{4}(x)$ Factor the expression: $sec^{2}(x) (tan^{2}(x) + 1)$ = $sec^{4}(x)$ Using the above note: $sec^{2}(x)$$sec^{2}(x)$ = $sec^{4}(x)$ $sec^{4}(x) = sec^{4}(x)$