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

Aman Bansal
592 Points
12 years ago

Dear Arnab,

Use Formula,

and,

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

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Thanks

Aman Bansal

Fyu
11 Points
7 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!