Vereenvoudig die volgende tot 'n enkele trigonometriese verhouding: 4.1 cos θ (tan θ + cot θ) 4.2 sin²(180° + B) · cosec (π - B) sec(2π - B) · cos(180° - B) - NSC Technical Mathematics - Question 4 - 2021 - Paper 1

For this part, we again use trigonometric identities:

1. From the periodic properties, we know that: $\sin(180° + B) = -\sin B.$ Therefore, $\sin^2(180° + B) = \sin^2 B.$

2. The cosecant of an angle is the reciprocal of sine: $\cosec(π - B) = \frac{1}{\sin(π - B)} = \frac{1}{\sin B}.$ Combining these, we have: $\sin^2(180° + B) · \cosec(π - B) = \sin^2 B · \frac{1}{\sin B} = \sin B.$

3. Next, we simplify the second expression: $\sec(2π - B) · \cos(180° - B).$ Using the identities: $\sec(2π - B) = \sec B$ and $\cos(180° - B)= -\cos B.$ Thus, $\sec(2π - B) · \cos(180° - B) = \sec B · (-\cos B) = -1.$