Question

Verify the following identity: (csc theta -cot theta )/(sec theta -1) A. sec theta B. cos theta C. cot theta D. sin theta

Answer 1

Answer:

C. cot theta

Step-by-step explanation:

(csc theta -cot theta )/(sec theta -1)

csc = 1/ sin

cot = cos / sin

sec = 1 / cos

Let x = theta

(1/ sin x -cos x / sin x )/(1/ cos x -1)

Getting a common denominator in the denominator and combining terms

(1- cos x)/ sinx  / ( 1 - cos x) / cos x

(1- cosx)      (1- cosx)

----------- ÷ ------------

sinx            cos x

Copy dot flip

(1- cosx)       cosx

----------- * ------------

sinx            1 -cos x

Cancel like terms

cos x / sin x

cos / sin = cot

cot x

cot theta