Question

how to solve this identity step by step:
cosx +1/ tan^2x = cosx/secx -1

Answer 1

how to solve this identity step by step:

$$\cos x + 1 / \tan^ {2} x = \cos x / \sec x - 1$$

Solution

We can prove, that it is not identity. For this let's consider value of $x$ :

$$x _ {1} = \frac {\pi}{4};$$

For $x_{1}$ the left side is:

$$\cos (x) + \frac {1}{\tan^ {2} x} = \frac {\sqrt {2}}{2} + \frac {1}{1} = \frac {2 + \sqrt {2}}{2}$$

The right side is:

$$\frac {c o x (x)}{\sec (x)} - 1 = \frac {\frac {\sqrt {2}}{\frac {2}{\sqrt {2}}}}{\sqrt {2}} - 1 = \frac {1}{2} - 1 = - \frac {1}{2}$$

Obviously:

$$\frac {2 + \sqrt {2}}{2} \neq - \frac {1}{2}$$

This is not the identity.

NB: It's the equation, solving which is not easy at all. And the solution lies in complex plane