Home » Simplify (cos^{2} x (sec^{2} x + sec^{2} x tan^{2} x))

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

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)

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