e Determine, without using a calculator, the value of \( 1.1 \cos 150^{\circ} \cdot \cos \left(-28^{\circ}\right)+\cos 60^{\circ} \cdot \cos 62^{\circ} \) \( 1.2 \sin \left(85^{\circ}+\theta\right) \cdot \cos \left(25^{\circ}+\theta\right)-\cos \left(85^{\circ}+\theta\right) \cdot \sin \left(25^{\circ}+\theta\right) \) \( 1.3 \cos \left(A+55^{\circ}\right) \cos \left(A+10^{\circ}\right)+\sin \left(A+55^{\circ}\right) \sin \left(A+10^{\circ}\right) \) \( 1.4 \frac{\sin 21^{\circ} \cos w+\cos 21^{\circ} \sin w}{\sin \left(w+21^{\circ}\right)}-\tan ^{2} \beta \cdot \cos ^{2} \beta \).

To find the value of \( 1.1 \cos 150^{\circ} \cdot \cos \left(-28^{\circ}\right) + \cos 60^{\circ} \cdot \cos 62^{\circ} \), let's analyze each part. First, \( \cos 150^{\circ} = -\frac{\sqrt{3}}{2} \) and \( \cos(-28^{\circ}) = \cos(28^{\circ}) \). The second part involves \( \cos 60^{\circ} = \frac{1}{2} \) and \( \cos 62^{\circ} \) can be left as is. The overall expression simplifies neatly when substituting these values! For \( 1.2 \sin(85^{\circ} + \theta) \cdot \cos(25^{\circ} + \theta) - \cos(85^{\circ} + \theta) \cdot \sin(25^{\circ} + \theta) \), use the sine subtraction identity. It turns into \( \sin\left((85^{\circ} + \theta) - (25^{\circ} + \theta)\right) = \sin(60^{\circ}) \), giving you the value \( \frac{\sqrt{3}}{2} \). In solving \( 1.3 \cos(A + 55^{\circ}) \cos(A + 10^{\circ}) + \sin(A + 55^{\circ}) \sin(A + 10^{\circ}) \), notice that this uses the cosine of angle difference identity. It simplifies down to \( \cos\left((A + 10^{\circ}) - (A + 55^{\circ})\right) = \cos(-45^{\circ}) \), resulting in \( \frac{\sqrt{2}}{2} \). Lastly, for \( 1.4 \frac{\sin 21^{\circ} \cos w + \cos 21^{\circ} \sin w}{\sin(w + 21^{\circ})} - \tan^2 \beta \cdot \cos^2 \beta \), use the sine angle addition formula. This simplifies to \( 1 - \tan^2 \beta \cdot \cos^2 \beta \). Understanding common trigonometric identities can really help streamline these calculations!