Login

prove that : (cos 2x * cos 3x - cos 2x * cos 7x + cos x * cos 10 x) /( sin 4x * sin 3x - sin 2x * sin 5x + sin 4x * sin 7x) = cot 6x * cot 5x 

Dear Student ,
 
Please find below the solution to the asked query :

LHScos 2x cos 3x-cos 2x cos 7x+cos x cos 10 xsin 4x sin 3x-sin 2x sin 5x+sin 4x sin 7x=2 cos 2x cos 3x-2 cos 2x cos 7x+2 cos x cos 10 x2 sin 4x sin 3x-2 sin 2x sin 5x+2 sin 4x sin 7x=cos 5x+cos x-cos 9x-cos 5x+cos 11x+cos 9xcos x-cos 7x-cos 3x+cos 7x+cos 3x-cos 11x   Since 2 cos x cos y=cosx+y+cosx-y and 2 sin x sin y=cosx-y-cosx+y=cos x+cos 11xcos x-cos 11x=2 cos 6x cos 5x2 sin 6x sin 5x     Since cos x+ cos y=2 cosx+y2cosx-y2 and cos x-cos y=-2 sinx+y2sinx-y2=cot 6x cot 5x=RHSHence Proved.
 
Hope this information will clear your doubts about the topic .
If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible .

Regards

  • 7
View Full Answer
What are you looking for?