Calculate without using tables Tan 45° + Cos 60°

Analyze the question: You are asked to find the value of tan 45° + cos 60° using exact values, with no tables.

Concept: Some special angles have exact trigonometric values you should memorize:

| Angle | sin | cos | tan | |---|---|---|---| | 30° | 1/2 | √3/2 | 1/√3 | | 45° | 1/√2 | 1/√2 | 1 | | 60° | √3/2 | 1/2 | √3 |

Solution:

• tan 45° = 1
• cos 60° = 1/2

So:

tan 45° + cos 60° = 1 + 1/2 = 1½

Checking the options:

• A and D contain square roots, so they don't match.
• B (½) is only the cos 60° part.
• E (2) would require cos 60° = 1, which is wrong.
• C (1½) matches our result.

Tip: Draw a 45°-45°-90° triangle with sides 1, 1, √2 for tan 45° = 1. For 30° and 60°, use an equilateral triangle of side 2 cut in half, which gives sides 1, √3, 2. Cos 60° = adjacent/hypotenuse = 1/2. Rebuilding the triangle quickly in the exam saves you from forgetting values.