Question

Prove the following identities :
$co{s}^{4}A-co{s}^{2}A=si{n}^{4}A-si{n}^{2}A$

Answer 1

We have,
LHS = $co{s}^4-co{s}^{2}A$

$\Rightarrow$ LHS = $co{s}^{2}A$ ($co{s}^{2}A-1$)

$\Rightarrow$ LHS = $-co{s}^{2}A$ ($1-co{s}^{2}A$ )

$\Rightarrow$ LHS = $-co{s}^{2}A$ $si{n}^{2}A$ = $-(1-si{n}^{2}A$ )$si{n}^{2}A$$=-si{n}^{2}A+si{n}^{4}A$

$\Rightarrow$ LHS = $si{n}^{4}A$$-si{n}^{2}A$ = RHS