Question

solve the following equation sec x Cos 5 x + 1 = 0 and find its number of solutions

Answer 1

Cos5xsecx+1=0=> Cos5x= -1/secx= -cosx .
=>Cos5x+Cosx=0=> 2Cos3xCos2x=0=>either Cos3x=0 or Cos2x=0. Within the interval of 0to 2π, Cosx becomes zero at x=90°,270°. Cos3x=Cos90°,Cos270°,Cos450°,Cos630°,Cos810°,
Cos990°=> x=30°,90°,150°,210°,270°,330°. Cos2x=Cos90°,Cos270°,Cos450°,Cos630°.=>x=45°,135°,225°,315°. x=30°,45°,90°,135°,150°,210°,225°,270°,315°,330°. I hope it helps you...