Question

The value of ${\sec }^{2}A{\tan }^{2}B-{\tan }^{2}A{\sec }^{2}B$ is

• A. ${\tan }^{2}B-{\tan }^{2}A$
• B. ${\sec }^{2}B+{\sec }^{2}A$
• C. ${\tan }^{2}B-{\sec }^{2}A$
• D. ${\sec }^{2}B-{\tan }^{2}A$

Answer 1

The correct option is A ${\tan }^{2}B-{\tan }^{2}A$

$(1+{\tan }^{2}A){\tan }^{2}B-{\tan }^{2}A(1+{\tan }^{2}B)$

$={\tan }^{2}B+{\tan }^{2}A{\tan }^{2}B-{\tan }^{2}A-{\tan }^{2}A{\tan }^{2}B$

$={tan}^{2}B-{tan}^{2}A\left[A\right]$