By, means of an example, show that sin(A + B) ≠ sin A + sin B.

If 20° + x is an acute angle and cos(20° + x) = sin 60°, then find the value of x.

If A = 60° and B = 30°, verify that

(i) sin(A + B) = sin A cos B + cos A sin B

(ii) cos(A + B) = cos A cos B - sin A sin B

(iii) sin(A - B) = sin A cos B - cos A sin B

(iv) tan(A - B) = $\dfrac{\text{tan A - tan B}}{\text{1 + tan A tan B}}.$

If 3 sin² θ = $2\dfrac{1}{4}$ and θ is less than 90°, find the value of θ.