Question 94

What is the simplified value of (sec A + cos A)(sec A - cos A)?

Solution

Expression : $$(secA+cosA)(secA-cosA)$$

= $$(\frac{1}{cosA}+cosA)(\frac{1}{cosA}-cosA)$$

= $$(\frac{1+cos^2A}{cosA})(\frac{1-cos^2A}{cosA})$$

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

= $$\frac{sin^2A}{cos^2A}+sin^2A$$

= $$tan^2A+sin^2A$$

=> Ans - (D)

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