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

User Merc
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1 Answer

6 votes

Answer:

C. cot theta

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)

----------- รท ------------

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

User Spume
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