(Solved): 1. Verify the identity \[ \cos ^{4} x-\sin ^{4} x=\cos 2 x \] 2. Verify the identity \( \frac{\sin ...

1. Verify the identity \[ \cos ^{4} x-\sin ^{4} x=\cos 2 x \] 2. Verify the identity \( \frac{\sin 3 x}{\sin 2 x}=2 \cos x-\frac{1}{2} \sec x \) 3. Write in terms of first powers of cosine \( \sin ^{4} x \) 4. Use half-angle formulas to calculate \( \cos 112.5^{\circ} \).