Prove that:(i) sin A+sin 3Acos A-cos 3A=cot A(ii) sin 9A-sin 7Acos 7A-cos 9A=cot 8A(iii) sin A-sin Bcos A+cos B=tanA-B2(iv) sin A+sin Bsin A-sin B = tan A+B2 cot A -B2 (v) cos A+cos Bcos B-cos A=cot A+B2 cot A-B2

Prove that:(i) sin A+sin 3Acos A-cos 3A=cot A(ii) sin 9A-sin 7Acos 7A-

1.	Prove that:(i) sin A+sin 3Acos A-cos 3A=cot A(ii) sin 9A-sin 7Acos 7A-cos 9A=cot 8A(iii) sin A-sin Bcos A+cos B=tanA-B2(iv) sin A+sin Bsin A-sin B = tan A+B2 cot A -B2 (v) cos A+cos Bcos B-cos A=cot A+B2 cot A-B2
Answer» Prove that: (i) $\frac{\sin A + \sin 3 A}{\cos A - \cos 3 A} = \cot A$ (ii) $\frac{\sin 9 A - \sin 7 A}{\cos 7 A - \cos 9 A} = \cot 8 A$ (iii) $\frac{\sin A - \sin B}{\cos A + \cos B} = \tan \frac{A - B}{2}$ (iv) $\frac{\sin A + \sin B}{\sin A - \sin B} = \tan (\frac{A + B}{2}) \cot (\frac{A - B}{2})$ (v) $\frac{\cos A + \cos B}{\cos B - \cos A} = \cot (\frac{A + B}{2}) \cot (\frac{A - B}{2})$