Question

State whether the statement is true/false

$\frac{\cos 2A\cos 3A-\cos 2A\cos 7A+\cos A\cos 10A}{\sin 4A\sin 3A-\sin 2A\sin 5A+\sin 4A\sin 7A}=\cot A\cot 5A$

• A. True
• B. False

Answer 1

The correct option is B False

Given

LHS

$⟹\frac{\cos 2A\cos 3A-\cos 2A\cos 7A+\cos A\cos 10A}{\sin 4A\sin 3A-\sin 2A\sin 5A+\sin 4A\sin 7A}$

$⟹\frac{\cos 5A+\cos A-\cos 9A-\cos 5A+\cos 11A+\cos 9A}{\cos A-\cos 7A-\cos 3A+\cos 7A+\cos 3A-\cos 11A}$

$⟹\frac{\cos A+\cos 11A}{\cos A-\cos 11A}$

$⟹\frac{2\cos 6A\cos 5A}{2\sin 6A\sin 5A}$

$⟹\cot 6A\cot 5A$