Find all x in the interval \(\displaystyle{\left({0},{\frac{{\pi}}{{{2}}}}\right)}\)

Blaine Jimenez

Blaine Jimenez

Answered question

2022-04-14

Find all x in the interval (0,π2) such that
31sinx+3+1cosx=42

Answer & Explanation

o2z1zsjj0

o2z1zsjj0

Beginner2022-04-15Added 10 answers

Rewrite it in the form
22(3122)cos+3+122sinx)=22sin2x
For ϕ=arcsin3122 it implies
sin(x+ϕ)=sin2x
i.e x+ϕ=2x+2πn or x+ϕ=π2x+2πn, nZ. Therefore, the only solutions in (0,π2) are ϕ and πϕ3.

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