If \(\frac{cos\,x}{1+cosec\,x}+\frac{cos\,x}{cosec\,x-1}=2\) which on

1.	If \(\frac{cos\,x}{1+cosec\,x}+\frac{cos\,x}{cosec\,x-1}=2\) which one of the following is one of the values of x ?(a) \(\frac{π}{2}\) (b) \(\frac{π}{3}\)(c) \(\frac{π}{4}\) (d) \(\frac{π}{6}\)
Answer» (c) \(\fracπ4\) \(\frac{cos\,x}{1+cosec\,x}+\frac{cos\,x}{cosec\,x-1}=2\) ⇒ \(\frac{cos\,x(cosec\,x-1)+cos\,x(1+cosec\,x)}{cosec^2\,x-1}=2\) ⇒ \(\frac{2\,cos\,x\,cosec\,x}{cot^2\,x}=2\) ⇒ \(\frac{cos\,x}{sin\,x}\times\frac{sin^2\,x}{cos^2\,x}=1\) ⇒ tan \(x\) = 1 ⇒ tan\(x\) = tan \(\fracπ4\) ⇒ \(x\) = \(\fracπ4\).

If \(\frac{cos\,x}{1+cosec\,x}+\frac{cos\,x}{cosec\,x-1}=2\) which one of the following is one of the values of x ?(a) \(\frac{π}{2}\) (b) \(\frac{π}{3}\)(c) \(\frac{π}{4}\) (d) \(\frac{π}{6}\)

Answer»

(c) \(\fracπ4\)

\(\frac{cos\,x}{1+cosec\,x}+\frac{cos\,x}{cosec\,x-1}=2\)

⇒ \(\frac{cos\,x(cosec\,x-1)+cos\,x(1+cosec\,x)}{cosec^2\,x-1}=2\)

⇒ \(\frac{2\,cos\,x\,cosec\,x}{cot^2\,x}=2\)

⇒ \(\frac{cos\,x}{sin\,x}\times\frac{sin^2\,x}{cos^2\,x}=1\)

⇒ tan \(x\) = 1 ⇒ tan\(x\) = tan \(\fracπ4\) ⇒ \(x\) = \(\fracπ4\).