Solve the equation \(\displaystyle{\sin{{\left({11}{x}\right)}}}{\sin{{\left({x}\right)}}}={\cos{{\left({10}{x}\right)}}}\)

Amya Horn

Amya Horn

Answered question

2022-03-23

Solve the equation
sin(11x)sin(x)=cos(10x)

Answer & Explanation

Carter Lin

Carter Lin

Beginner2022-03-24Added 13 answers

As 2sinAsinB=cos(AB)cos(A+B)
2sin11xsinx=cos(10x)cos12x
We have 2sin11sinx=2cos10x
2cos10x=cos(10x)cos12x
cos10x=cos12x=cos(π12x) as cos(πy)=cosy
10x=2nπ±(π12x) where n is any integer

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