Question

What is cos3x-sin6x-cos9x/sin9x-cos6x-sin3x​

Answer 1

Answer:

Step-by-step explanation:

Cosx + Cosy = 2Cos(½x+½y)Cos(½x-½y)

Cosx - Cosy = -2Sin(½x+½y)Sin(½x-½y)

Sinx + Siny = 2Sin(½x+½y)Cos(½x-½y)

Sinx - Siny = 2Cos(½x+½y)Sin(½x-½y)

a. (cos3x - sin6x - cos9x) / (sin9x - cos6x - sin3x) = tan6x

(cos3x - cos9x - sin6x) / (sin9x - sin3x - cos6x) = tan6x

(2Sin6x.Sin3x - Sin6x) / (2Cos6x.Sin3x - Cos6x) = Tan6x

[Sin6x(2Sin3x - 1)] / [Cos6x(2Sin3x - 1)] = Tan6x

Sin6x / Cos6x = Tan6x

Tan6x = Tan6x

Terbukti

b. (sin3x + sin5x + sin7x + sin9x) / (cos3x + cos5x + cos7x + cos9x) = tan6x

[(sin3x+sin5x)+(sin7x+sin9x)] / [(cos3x+cos5x)+(cos7x+cos9x)] = tan6x

[2sin4xCosx + 2sin8xCosx] / [2cos4xCosx + 2cos8xCosx] = tan6x

[2Cosx(sin4x+sin8x)] / [2Cosx(cos4x+cos8x)] = tan6x

(sin4x+sin8x) / (cos4x+cos8x) = tan6x

(2Sin6xCos2x) / (2Cos6xCos2x) = tan6x

Sin6x / Cos6x = tan6x

Tan6x = Tan6x