Question

If $P_n={\cos }^{n}x+{\sin }^{n}x,$ then $2P_6-3P_4+1=$

• A. 2
• B. 3
• C. \N
• D. 1

Answer 1

The correct option is C \N

$2P_6-3P_4+1=2({\cos }^{6}x+{\sin }^{6}x)-3({\cos }^{4}x+{\sin }^{4}x)+1=2\left(\right(1-3{\sin }^{2}x{\cos }^{2}x)-3[({\sin }^{2}x+{\cos }^{2}x{)}^2-2{\sin }^{2}x{\cos }^{2}x]+1$
$=2-6{\sin }^{2}x{\cos }^{2}x-3(1-2{\sin }^{2}x{\cos }^{2}x)+1=0$