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
Correct Answer: Option C
Explanation
(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)