I have an equation that I'm trying to solve: \sin x+\sqrt{3}\cos

tumahimikgjr

tumahimikgjr

Answered question

2022-03-01

I have an equation that I'm trying to solve:
sinx+3cosx=1

Answer & Explanation

Ulgelmorgs

Ulgelmorgs

Beginner2022-03-02Added 8 answers

There's a nice trick:
sinx+3cosx=1
=2(12sinx+32cosx)
=2(cos(π3+2kπ)sinx+sin(π3+2kπ)cosx)
=2sin(x+π3+2kπ)=1
Then
sin(x+π3+2kπ)=12

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