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sin 5x * cos 3x = sin 9x * cos 7x. Find the general solution of the equation.

sin 5x * cos 3x = sin 9x * cos 7x. Find the general solution of the equation.

Grade:11

2 Answers

Aman Bansal
592 Points
10 years ago

Dear Arnab,

Use Formula,

sumSines1.gif

and,

sumCosPlus.gif

to reduce the expression as sum terms and then it can be easily solved.

Best Of Luck...!!!!

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Fyu
11 Points
6 years ago
   sin5x.cos3x=sin6x.cos2x                                             
   Multiplying both the sides by 2
   2sin5x.cos3x=2sin6x.cos2x                                        
   sin(5x+3x)+sin(5x-2x)=sin(6x+2x)+sin(6x-2x)
   sin8x+sin2x=sin8x+sin4x    
   sin2x-sin4x=0 
   2sin(2x-4x/2)cos(2x+4x/2)                                          
   -2sinxcos3x=0                        
    X=npi         Or 3x=(2n+1)pi/2 -> x=(2n+1)pi/6
       Hope this helps you!  
 
 
 
 

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