Question

Sqrt (1+cos(x)/1-cos(X))=cosec(X)+cot(X) then X lies in which quadrants
A)I,II. B)II,III. C)I,III. D)I,IV

Answer 1

Answer:

cosec x+cot x=a……………….(1)

we know that:-

cosec^2 x - cot^2 x = 1

or. (cosec x+cot x).(cosec x-cot x)= 1. , putting cosec x +cot x= a

or. (a).(cosec x-cot x)=1

or. cosec x- cot x. = 1/a…………….(2)

by adding and subtracting eqn. (1)and (2)

2.cosec x= (a+1/a). => 2. cosec x =(a^2+1)/a……………(3)

2.cot x = (a-1/a). => 2.cot x =(a^2-1)/a…………………….(4)

Dividing eqn. (4) by (3).

(2.cot x)/(2.cosec x). = {(a^2-1)/a}/{(a^2+1)/a}.

( cos x/sin x)/(1/sin x). = (a^2–1)/(a^2+1).

cos x= (a^2-1)/(a^2+1). Answer.

Step-by-step explanation:

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