Evaluate:
cos 45°/sec 30°+cosec30°​

Look at the trigonometry table for special angles.

From here, substitute the values in:

Simplify:

Rationalize:

And this is your answer.

Alright, the angles ∠A and ∠B  are corresponding angles meaning they have the same degree value!

∠A = 8x - 8°

∠B = 5x + 25°

To find ∠B, however, we're going to need to know the value of x !

The only way we're going to find what x is, is to set the angles equal to each other ...

Do as follows:

∠A = ∠B

8x - 8 = 5x + 25

Combine like terms

8x = 5x + 25 + 8

8x = 5x + 33

8x - 5x = 33

3x = 33

x = 11

Now plug in x to find the value of ∠B

∠B = 5(11) + 25°

∠B = 55 + 25°

∠B = 80°