Question

sinx - 4sin³x + cosx=0

 

Answer 1

\(\sin x-4\sin^3x+cosx=0\)sinx-4sin³x+cosx=0 \(\Rightarrow\) \(\frac{\text{sin x}-4\sin^3x+\cos x}{\sin x}\)=0 \(\Leftrightarrow\) 1-4sin²x+\(\frac{cosx}{sinx}\)=0\(\Leftrightarrow\)1 - \(\frac{4\tan^2x}{tan^2x+1}\)+\(\frac{1}{\tan x}\)=0 \(\Leftrightarrow\) \(\frac{\left(\tan^2x+1\right)\tan x-4\tan^3x+1}{\tan x}\) =0

\(\Rightarrow\)\(\left(\tan^2x+1\right)\tan x-4\tan^3x+1\)= 0 \(\Leftrightarrow\) \(-3\tan^2x+\tan^2x+\tan x+1\)=0 \(\Rightarrow\) tanx=1 \(\Leftrightarrow\) x=45^o