Question

Find the value of: $(1-{\sin }^{2}x){\sec }^{2}x$

• A. $\frac{1}{2}$
• B. 1
• C. 0
• D. -1

Answer 1

Answer: (B)

1

we know ${\sin }^{2}x+{\cos }^{2}x=1$

${\cos }^{2}x=1-{\sin }^{2}x......\left(1\right)$

Given,

$(1-{\sin }^{2}x){\sec }^{2}x$
$={\cos }^{2}x{\sec }^{2}x$ from $\left(1\right)$
$={\cos }^{2}x\times \frac{1}{{\cos }^{2}x}$ $({\sec }^{2}x\times {\cos }^{2}x=1)$
$=1$