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Prove that:
cos A + cos 3A + cos 5A + cos 7A = 4 cos A cos 2A cos 4A
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
`sin A + sin 2A + sin 4A + sin 5A = 4 cos (A/2) cos((3A)/2)sin3A`
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
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Prove that:
sin 3A + sin 2A − sin A = 4 sin A cos \[\frac{A}{2}\] \[\frac{3A}{2}\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
cos 20° cos 100° + cos 100° cos 140° − 140° cos 200° = −\[\frac{3}{4}\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\sin\frac{x}{2}\sin\frac{7x}{2} + \sin\frac{3x}{2}\sin\frac{11x}{2} = \sin 2x \sin 5x .\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that \[\cos x \cos \frac{x}{2} - \cos 3x \cos\frac{9x}{2} = \sin 7x \sin 8x\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin A + \sin 3A}{\cos A - \cos 3A} = \cot A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin 9A - \sin 7A}{\cos 7A - \cos 9A} = \cot 8A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin A - \sin B}{\cos A + \cos B} = \tan\frac{A - B}{2}\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin A + \sin B}{\sin A - \sin B} = \tan \left( \frac{A + B}{2} \right) \cot \left( \frac{A - B}{2} \right)\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\cos A + \cos B}{\cos B - \cos A} = \cot \left( \frac{A + B}{2} \right) \cot \left( \frac{A - B}{2} \right)\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\cos 3A + 2 \cos 5A + \cos 7A}{\cos A + 2 \cos 3A + \cos 5A} = \frac{\cos 5A}{\cos 3A}\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin A + \sin 3A + \sin 5A}{\cos A + \cos 3A + \cos 5A} = \tan 3A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\cos 4A + \cos 3A + \cos 2A}{\sin 4A + \sin 3A + \sin 2A} = \cot 3A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin 3A + \sin 5A + \sin 7A + \sin 9A}{\cos 3A + \cos 5A + \cos 7A + \cos 9A} = \tan 6A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin 5A - \sin 7A + \sin 8A - \sin 4A}{\cos 4A + \cos 7A - \cos 5A - \cos 8A} = \cot 6A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin 5A \cos 2A - \sin 6A \cos A}{\sin A \sin 2A - \cos 2A \cos 3A} = \tan A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin 11A \sin A + \sin 7A \sin 3A}{\cos 11A \sin A + \cos 7A \sin 3A} = \tan 8A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin 3A \cos 4A - \sin A \cos 2A}{\sin 4A \sin A + \cos 6A \cos A} = \tan 2A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
Prove that:
\[\frac{\sin A \sin 2A + \sin 3A \sin 6A}{\sin A \cos 2A + \sin 3A \cos 6A} = \tan 5A\]
Chapter: [3] Trigonometric Functions
Concept: undefined >> undefined
Concept: undefined >> undefined
