**Answer**

**(i) (B) is correct.**

9 sec^{2}A - 9 tan^{2}A

= 9 (sec^{2}A - tan^{2}A)

= 9×1 = 9 (∵ sec2 A - tan2 A = 1)

**(ii) (C) is correct**

(1 + tan θ + sec θ) (1 + cot θ - cosec θ)

= (1 + sin θ/cos θ + 1/cos θ) (1 + cos θ/sin θ - 1/sin θ)

= (cos θ+sin θ+1)/cos θ × (sin θ+cos θ-1)/sin θ

= (cos θ+sin θ)^{2}-1^{2}/(cos θ sin θ)

= (cos^{2}θ + sin^{2}θ + 2cos θ sin θ -1)/(cos θ sin θ)

= (1+ 2cos θ sin θ -1)/(cos θ sin θ)

= (2cos θ sin θ)/(cos θ sin θ) = 2

**(iii) (D) is correct.**

(secA + tanA) (1 - sinA)

= (1/cos A + sin A/cos A) (1 - sinA)

= (1+sin A/cos A) (1 - sinA)

= (1 - sin^{2}A)/cos A

= cos^{2}A/cos A = cos A

**(iv) (D) is correct.**

1+tan^{2}A/1+cot^{2}A

= (1+1/cot^{2}A)/1+cot^{2}A

= (cot^{2}A+1/cot^{2}A)×(1/1+cot^{2}A)

= 1/cot^{2}A = tan^{2}A