Find all solutions of the equation in the

Jasmine Todd

Jasmine Todd

Answered question

2022-04-02

Find all solutions of the equation in the interval [0,2π). Express your answer in terms of k, where k is any integer.
tan3θ+1=sec3θ

Answer & Explanation

Ishaan Stout

Ishaan Stout

Beginner2022-04-03Added 14 answers

Divide throughout by sec3θ to give sin3θ+cos3θ=1
Now observe that the LHS is basically 2sin(3θ+π4)
So,
sin(3θ+π4)=12
3θ+π4=π4+2kπ, kZ
In the required range, you have the solutions θ=0,2π3,4π3

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