The value of  is:

Given:

We need to find the value of:

Formula Used:

cos² θ + sin² θ = 1

Calculation:

Take the LCM of the two terms:

Expanding the numerator:

cos² 50° + (1 + 2sin 50° + sin² 50°)

Using the identity cos² θ + sin² θ = 1:

1 + (1 + 2sin 50°)

2 + 2sin 50°

Now, the expression becomes:

Factor out 2 from the numerator:

Cancel out the common term (1 + sin 50°):

2 / cos 50°

The value of 1 / cos 50° is sec 50°.

Therefore, the expression simplifies to: 2 sec 50°

∴ The value of the given expression is 2 sec 50°.