Question

Prove that: $si{n}^{4}A-co{s}^{4}A=2si{n}^{2}A-1$

Answer 1

LHS = $si{n}^{4}A-co{s}^{4}A$

$=(si{n}^{2}A{)}^2-(co{s}^{2}A{)}^2$

$=(si{n}^{2}A{)}^2-(1-si{n}^{2}A{)}^2$

$=(si{n}^{2}A{)}^2-(1+(si{n}^{2}A{)}^2-2si{n}^{2}A)$

$=2si{n}^{2}A-1$

$RHS=2si{n}^{2}A-1$

LHS = RHS