Question

cos^4A-sin^4A+1=2cos^2A​

Answer 1

Step-by-step explanation:

$cos^{4}A-sin^{4}A+1=2cos^{2}A.....(i)\\\\Consider$ $L.H.S;$

     We know that;

     $sin^{2}A=1-cos^{2}A$

    Squaring both sides;

     $(sin^{2}A)^{2}=(1-cos^{2}A)^{2} \\sin^{4}A=1 + cos^{4}A -2cos^{2}A$

   Put value of  $sin^{4}A$ into equation (i)

   $=cos^{4}A -(1+cos^{4}A-2cos^{2}A)+1\\ \\=cos^{4}A-1-cos^{4}A+2cos^{2}A +1\\\\=2cos^{2}A=R.H.S$