cos 45°sec 30° + cosec 30

Sure, let's solve this step by step:

1. First, we need to know the values of cos 45°, sec 30°, and cosec 30°.

2. The value of cos 45° is √2/2 or 0.7071.

3. The value of sec 30° is 2/√3 or 1.1547. Sec is the reciprocal of cos, so sec 30° = 1/cos 30°.

4. The value of cosec 30° is 2. Cosec is the reciprocal of sin, so cosec 30° = 1/sin 30°.

5. Now, substitute these values into the equation:

   cos 45°sec 30° + cosec 30° = (√2/2 * 2/√3) + 2

6. Simplify the equation:

   = (√2/√3) + 2

7. To make it easier, rationalize the denominator:

   = (√2*√3/3) + 2

   = √6/3 + 2

8. Convert 2 into a fraction with 3 as the denominator:

   = √6/3 + 6/3

9. Add the fractions:

   = (√6 + 6)/3

So, cos 45°sec 30° + cosec 30° = (√6 + 6)/3.