Question

prove that : given in photo
please do it hurry​

Answer 1

Answer:

Step-by-step explanation:

Formula will be used::

1. 2 sinA cosB = sin (A+B) + sin (A-B)  

2. 2 cosA cosB = cos (A+B) + cos (A-B)  

3. 2 sinA sinB = cos (A-B) - cos (A+B)  

4. sinx / cosx = tanx  

5. sinC - sinD = 2 cos ( (C+D) / 2 ) sin ( (C-D) / 2 )  

6. cosC + cosD = 2 cos ( (C+D) / 2 ) cos ( (C-D) / 2 )  

(sin8xcosx - sin6xcos3x) / (cos2xcosx - sin3xsin4x)  

= 2 (sin8xcosx - sin6xcos3x) / 2 (cos2xcosx - sin3xsin4x)  

= (2sin8xcosx - 2sin6xcos3x) / (2cos2xcosx - 2sin3xsin4x)  

= (sin9x + sin7x - (sin 9x + sin3x)) / (cos3x + cosx - (cosx - cos7x))  

= (sin7x - sin3x) / (cos7x + cos3x)  

= 2 cos5x sin2x / 2 cos5x cos2x  

= sin2x / cos2x  

= tan2x