Question

Find the value of ${\sec }^{2}x$ - ${\text{cosec}}^{2}x$.

• A. ${\tan }^{2}x$ + ${\cot }^{2}x$
• B. ${\cot }^{2}x$ - ${\tan }^{2}x$
• C. ${\tan }^{2}x$ - ${\cot }^{2}x$
• D. 1

Answer 1

The correct option is C

${\tan }^{2}x$ - ${\cot }^{2}x$

When we look at the options, they are in terms of $\tan x$ and $\cot x$.
So will try to express ${\sec }^{2}x$ and ${\text{cosec}}^{2}x$ in terms of $\tan x$ and $\cot x$.

We know ${\sec }^{2}x$ = 1 + ${\tan }^{2}x$ and

${\text{cosec}}^{2}x$ = 1 + ${\cot }^{2}x$

$\Rightarrow$ ${\sec }^{2}x$ - ${\text{cosec}}^{2}x$ = ${\tan }^{2}x$ - ${\cot }^{2}x$