Question

Prove that cos4A-sin4A=2cos2A-1

Answer 1

hope u get it
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Answer 2

cos4A-sin4A=2cos2A-1

proved below.

Step-by-step explanation:

Given:

$cos^4A-sin^4A=2cos^2A-1$

LHS=$cos^4A-sin^4A$

      =$[cos^2A]^2-[sin^2A]^2$

      =$[cos^2A+sin^2A][cos^2A-sin^2A]$        

      =$[1][cos^2A-(1-cos^2A)]$             [$cos^2A+sin^2A=1$]

      =$[cos^2A-1+cos^2A]$

      =$2cos^2A-1$

      =RHS.