Question on: JAMB Mathematics - 1991
Simplify cos2 x (sec2x + sec2 x tan2x)
A
tan x
B
tanx secx
C
\(\frac{1 + tan^2x}{sec^2x}\)
D
cosec2x
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Correct Option: C
cos2 x (sec2x + sec2 x tan2x)
= \(\frac{cos^2x}{cos^2x}\) x \(\frac{cos^2x sin^2x}{cos^2x cos^2x}\)
= \(\frac{1 + sin^2x}{cos^2x}\)
= \(\frac{1 + tan^2x}{sec^2x}\)
= \(\frac{cos^2x}{cos^2x}\) x \(\frac{cos^2x sin^2x}{cos^2x cos^2x}\)
= \(\frac{1 + sin^2x}{cos^2x}\)
= \(\frac{1 + tan^2x}{sec^2x}\)
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