Solve \cos x+8\sin x-7=0

broggesy9

broggesy9

Answered question

2022-04-20

Solve
cosx+8sinx7=0

Answer & Explanation

jeffster830gyz

jeffster830gyz

Beginner2022-04-21Added 21 answers

8sinx=7cosx
8(2sinx2cosx2)+7cosx
16sinx2cosx2=71+2sin2x2
16sinx2cosx2=6+2sin2x2
8sinx2cosx2=3+sin2x2
0=sin2x28sinx2cosx2+3
0=sinx2(sinx28cosx2)+3
Divide either sides by cos2x2
sin2x28sinx2cosx2+3=0
to get
tan2x28tanx2+3(1+tan2x2)=0
which on rearrangement is a Quadratic Equation in tanx2

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