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
jamb 1991mathematics

The correct answer is C. \(\sec^2 x\)

\(\cos^{2} x (\sec^{2} x + \sec^{2} x \tan^{2} x)\)

= \(\cos^{2} x \sec^{2} x + \cos^{2} x \sec^{2} x \tan^{2} x\)

= \(1 + \tan^{2} x\)

= \(1 + \frac{\sin^{2} x}{\cos^{2} x}\)

= \(\frac{\cos^{2} x + \sin^{2} x}{\cos^{2} x}\)

= \(\frac{1}{\cos^{2} x} = \sec^{2} x\)

Previous question Next question