Solve the equation \(\displaystyle{\cos{{\frac{{{4}{x}}}{{{3}}}}}}={\cos{{x}}}+{1}\)

Anika Boyd

Anika Boyd

Answered question

2022-03-22

Solve the equation
cos4x3=cosx+1

Answer & Explanation

Jared Kemp

Jared Kemp

Beginner2022-03-23Added 14 answers

There is a trigonometric method for solving cubic equations. Not very pleasant but doable. Applying the method to the case of
8t34t28t+3=0
Using A=12, B=1, C=38, Q=1336, R=43432, D=2576912
θ=cos1(432613)
the solutions are then
t1=16+133cos(θ3)
t2=16+132cos(θ+4π3)

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