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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
9 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
5 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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