\( \sin \alpha - i \cos \alpha \)

If the adjacent side measures 8 meters and the angle opposite to it is 45 degrees, calculate the length of the opposite side using trigonometric ratios.

What is the definition of the cosine function in relation to a right triangle using the adjacent side and hypotenuse?

If \( \tan \theta=\frac{20}{21} \), show that \( \frac{1-\sin \theta+\cos \theta}{1+\sin \theta+\cos \theta}=\frac{3}{7} \). (OR)

б) \( \sin ^{2} x \cdot \cos x=0 \) 2) \( \sin 3 x+\sin x=0 \)

d) \( \cos 2 x \cdot \cos x=\sin 2 x \cdot \cdot \sin x \)