If tan theta sec theta x 2 x 2 then what is the value of cos theta ........

Quantitative Aptitude ( CCS) Trignometry

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If tan θ + sec θ = (x - 2)/(x + 2), then what is the value of cos θ?

(x² - 1)/(x² + 1)

(2x² - 4)/(2x² + 4)

(x² - 4)/(x²+ 4)

(x²- 2)/(x²+ 2)

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Explanation:

If tanθ + secθ = (x - 2)/(x + 2) ----(1)
Then, secθ - tanθ = (x + 2)/(x - 2) ----(2)
By adding equation (1) and (2)
2secθ = (x + 2)/(x - 2) + (x - 2)/(x + 2)
⇒ 2secθ = {(x - 2)²+ (x + 2)²}/(x² - 4)
⇒ 2secθ = {2(x² + 4)}/(x²- 4)
∴ cosθ = (x² - 4)/(x² + 4)