Answer:
Step-by-step explanation:
[tex]\frac{1}{cos (2n+20)} =\frac{1}{cos(n+40)} \\cos (2n+20)=cos(n+40)\\cos (2n+20)-cos (n+40)=0\\-2 sin( \frac{2n+20+n+40}{2}) sin (\frac{2n+20-n-40}{2} )=0\\sin (\frac{3n}{2} +30)sin (\frac{n}{2} -10)=0\\either sin (\frac{3n}{2}+30)=0=sin180k\\\frac{3n}{2}=180k-30\\3n=360k-60\\n=120k-20,k ~is~an~integer.\\or~\frac{n}{2}-10=180k\\n=360 k+20\\where~k~is~an~integer.[/tex]
