tan(x+pi) + 2sin(x+pi)=0can you help prove this and make the left side equal the right?
Mathematics · Middle School · Tue Nov 03 2020
Answered on
For finding the solution we know the ideal formulas for trigonometry
tan(A+B)=tanA+tanB/1−tanA*tanB
Using the formula for the given equation But tanπ=0 hence
tan(x+π)=tanx+tanπ/1−tanx*tanπ = tanx
Also
sin(A+B)=sinA⋅cosB+cosA⋅in
Using the formula for the given equation
sin(x+π)=sinx⋅cosπ+cosx⋅sin(π)=−sinx
Using the formulas in a given equation
tan(x+π) + 2sin(x+π)=0
tan(x+π)=−2sin(x+π)
tanx=2sinx
Sinx/cosx=2sinx
sinx(1/cosx−2)=0
Hence we have that sinx=0
Sinx=sin(0)
x=0
And [(1/cosx)−2]=0
Cosx=½
For cos(½) value how lies between the interval [-1,1] so cos x=2⋅n⋅π±π/3 where n an integer.