Question

proove that 2sinxsin3x-1=0​

Answer 1

Answer:

I think this must not be a proof question rather it should be a question to find the value of x given the equation. why I think it must not be a proof question is simply put x = 0° and LHS will be -1 which is not equal to RHS. So, it is not correct for every value of x and hence not a proof question.

I am proceeding to solve it, given

2sinxsin3x - 1 = 0

cos(3x-x) - cos(3x+x) - 1 = 0

cos2x - cos4x - 1 = 0

cos2x - (2cos^2(2x) - 1) - 1 = 0

cos2x - 2cos^2(2x) = 0

cos2x(1 - 2cos2x) = 0

case 1

cos2x = 0 = cos π/2

2x = 2nπ +_ π/2

x= nπ +_ π/4

case 2

1-2cos2x = 0

cos2x = 1/2 = cosπ/6

2x = 2nπ +_ π/6

x= nπ +_ π/12