Answer:
11. d. cos A.
12. d. tan^2 A.
Step-by-step explanation:
11.
(sec A + tan A)(1 - sinA)
= sec A - sec A sin A + tan A - sin A tan A
Convert to sine's and cosine's using sec A = 1/ cos A and tan A = sin A / cos A:
= 1/cos A - sin A / cos A + sin A / cos A - sin^2 A / cos A
= 1 /cos A - sin^2 A / cos A
= (1 - sin^2 A) / cos A Using 1 - sin^ A = cos^2 A:
= cos^2 A / cos A
= cos A.
12.
Now sec^2 A = 1 + tan^2 A and cosec^2 A = 1 + cot^2 A so
(1 + tan^2 A) / (1 + cot^2 A)
= sec^2 A / cosec^2 A
= 1 / cos^2 A / 1 / sin^2 A
= sin^2 A / cos^2 A
= tan^2 A.
