Question

The number of solutions of the equation
sec x/1-cosx=1/1-cos x in[0,2π] is equal to:

Answer 1

Answer:

There is only one solution i.e. at x=0.

Step-by-step explanation:

Given : Expression $\frac{\sec x}{1-\cos x}=\frac{1}{1-\cos x}$

To find : The number of solutions of the equation  in [0,2π] ?

Solution :

Expression $\frac{\sec x}{1-\cos x}=\frac{1}{1-\cos x}$

First we solve the expression,

$\frac{\sec x(1-\cos x)}{1-\cos x}=1$

$\sec x=1$

From  [0,2π]  the sec x is 1 is only at 0.

So, $\sec x=\sec 0$

$x=0$

Therefore, There is only one solution i.e. at x=0.

Answer 2

Answer:

No solution

Step-by-step explanation:

secx/1-cosx =1/cosx

For 1−cosx =0⇒cosx =1 ..(1)

For 1−cosx =0⇒cosx =1 ..(1)Gives secx=1⇒cosx=1 ...(2)

For 1−cosx =0⇒cosx =1 ..(1)Gives secx=1⇒cosx=1 ...(2)From (1) and (2) we get no solution