If $$\frac{(1 + cosA)}{(1 - cosA)}$$ = x, then x is

Expression : $$\dfrac{(1 + cosA)}{(1 - cosA)}$$ = x

Multiplying both numerator and denominator by $$(1-cosA)$$

= $$\dfrac{1+cosA}{1-cosA} \times \dfrac{(1-cosA)}{(1-cosA)}$$

= $$\dfrac{1-cos^2A}{(1-cosA)^2} = \dfrac{sin^2A}{(1-cosA)^2}$$

Dividing both numerator and denominator by $$(cos^2A)$$

= $$\dfrac{sin^2A}{cos^2A}\div\dfrac{(1-cosA)^2}{cos^2A}$$

= $$tan^2A \div (\dfrac{1-cosA}{cosA})^2$$

= $$\dfrac{tan^2A}{(secA-1)^2}$$

=> Ans - (D)