3.1.
For any angle , sin² + cos² = 1 (main identity). Therefore, the answer is 1.

3.2.
Using the formula tan = sin/ cos, Nick could divide numbers in the sine-row by the numbers in the cosine-row.

3.3.
cot = cos/ sin

3.4.

3.5.
1) For any angle , tan ·cot = 1. However, 1/2 · 2/3 1.
2) For any angle , sin² + cos² = 1. However, (0.3)²+ (0.7)² 1.
3) If is in the range 45°<< 90°, then tan> 1. You can see this from the picture.

3.6.

3.7.

3.8.

3.9.
Let s=sin, c=cos. Then

1) tan + cot = s/c + c/s = (s² + c²) / (c-s) = 1/(c-s) = sec csc

2) 1+tan² = 1+s²/c² = (c²+s²) /c² = 1/c² = sec².

3) sin⁴-cos⁴=(s²-c²)(s²+c²) = s²-c^2.

3.10.

3.11.
f(30°) = sin 30° + cos 60° = ½ + ½ = 1.

3.12.

3.13.
tan (90° - ) = sin (90° - ) / cos(90° - ) = cos / sin = cot

3.14.

3.15.