3) If \( \mathrm{A}=20^{\circ} \) and \( \mathrm{B}=30^{\circ} \) determine the value of the following correct to 1 decimal place: \( \begin{array}{ll}\text { a) } 2 \sin B & \text { e) } \cos \left(90^{\circ}-B\right) \\ \text { b) } \frac{\sqrt{3}}{2} \cos B & \text { () } 2 \sin \left(2,5^{\circ}+A\right) \cos \left(2,5^{\circ}+A\right) \\ \text { e) } \cos (A+2 B) & \text { g) } \cos ^{2}(A)+\sin ^{2}(A)\end{array} \)

Let's calculate each of the expressions step by step based on the provided angles \( A = 20^\circ \) and \( B = 30^\circ \). **a)** \( 2 \sin B = 2 \sin(30^\circ) = 2 \times \frac{1}{2} = 1.0 \) **b)** \( \frac{\sqrt{3}}{2} \cos B = \frac{\sqrt{3}}{2} \cos(30^\circ) = \frac{\sqrt{3}}{2} \times \frac{\sqrt{3}}{2} = \frac{3}{4} = 0.75 \) **c)** \( 2 \sin(2.5^\circ + A) \cos(2.5^\circ + A) = \sin(2(2.5^\circ + 20^\circ)) = \sin(45^\circ) = \frac{\sqrt{2}}{2} \approx 0.707 \) **d)** \( \cos(A + 2B) = \cos(20^\circ + 60^\circ) = \cos(80^\circ) \approx 0.1736 \) **e)** \( \cos^2(A) + \sin^2(A) = 1 \) (This is the Pythagorean identity) Now rounding the values to one decimal place, we have: - a) \( 1.0 \) - b) \( 0.8 \) - c) \( 0.7 \) - d) \( 0.2 \) - e) \( 1.0 \) Here are the final results rounded to one decimal place: - a) \( 1.0 \) - b) \( 0.8 \) - c) \( 0.7 \) - d) \( 0.2 \) - e) \( 1.0 \) - g) \( 1.0 \)