This expression: \(\displaystyle{\cos{{\left({4}{x}\right)}}}{\cos{{\left({3}{x}\right)}}}-{4}{\sin{{\left({x}\right)}}}{\sin{{\left({3}{x}\right)}}}{\cos{{\left({x}\right)}}}{\cos{{\left({2}{x}\right)}}}\)

Gustavo Lam

Gustavo Lam

Answered question

2022-04-10

This expression:
cos(4x)cos(3x)4sin(x)sin(3x)cos(x)cos(2x)

Answer & Explanation

Gonarsu2dw8

Gonarsu2dw8

Beginner2022-04-11Added 19 answers

Notice, use the trig identity 2sinAcosA=sin2A as follows
cos(4x)cos(3x)4sin(x)sin(3x)cos(x)cos(2x)
=cos(4x)cos(3x)2(2sin(x)cos(x))sin(3x)cos(2x)
=cos(4x)cos(3x)2sin(2x)sin(3x)cos(2x)
=cos(4x)cos(3x)sin(4x)sin(3x)
Applying cosAcosBsinAsinB=cos(A+B)
=cos(4x+3x)
=cos7x

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