Simplify \(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)
A
tan x
B
tanx secx
C
\(\sec^2 x\)
D
cosec2x
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)
= \(\cos^{2} x \sec^{2} x + \cos^{2} x \sec^{2} x \tan^{2} x\)
= \(1 + \tan^{2} x\)
= \(1 + \frac{\sin^{2} x}{\cos^{2} x}\)
= \(\frac{\cos^{2} x + \sin^{2} x}{\cos^{2} x}\)
= \(\frac{1}{\cos^{2} x} = \sec^{2} x\)
Source: Myschool Past Questions Archive (Record #31421)