JAMB - Mathematics (1991 - No. 34)
Simplify \(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)
tan x
tanx secx
\(\sec^2 x\)
cosec2x
Explanation
\(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)
= \(\cos^{2} x \sec^{2} x + \cos^{2} x \sec^{2} x \tan^{2} x\)
= \(1 + \tan^{2} x\)
= \(1 + \frac{\sin^{2} x}{\cos^{2} x}\)
= \(\frac{\cos^{2} x + \sin^{2} x}{\cos^{2} x}\)
= \(\frac{1}{\cos^{2} x} = \sec^{2} x\)
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