Trigonometric series of the form sin(A−B)cosA⋅cosB+sin(B−C)cosB⋅cosC+sin(C−D)cosC⋅cosD =tanA−tanD As we know that, sin(A−B)cosA⋅cosB=tanA−tanB Based on the above given information, find sum of the series sinxcos3x+sin3xcos9x+sin9xcos27x+⋯ upto n terms

Trigonometric series of the form sin(A−B)cosA⋅cosB+sin(B−C)cosB�

1.	Trigonometric series of the form sin(A−B)cosA⋅cosB+sin(B−C)cosB⋅cosC+sin(C−D)cosC⋅cosD =tanA−tanD As we know that, sin(A−B)cosA⋅cosB=tanA−tanB Based on the above given information, find sum of the series sinxcos3x+sin3xcos9x+sin9xcos27x+⋯ upto n terms
Answer» Trigonometric series of the form $\frac{sin (A - B)}{cos A \cdot cos B} + \frac{sin (B - C)}{cos B \cdot cos C} + \frac{sin (C - D)}{cos C \cdot cos D}$ $= tan A - tan D$ As we know that, $\frac{sin (A - B)}{cos A \cdot cos B} = tan A - tan B$ Based on the above given information, find sum of the series $\frac{sin x}{cos 3 x} + \frac{sin 3 x}{cos 9 x} + \frac{sin 9 x}{cos 27 x} + \dots$ upto $n$ terms