Question

prove that:
$\frac{ { \left(1-2 { \left( \sin ( x ) \right) }^{ 2 } \right) }^{ 2 } }{ { \left( \cos ( x ) \right) }^{ 4 } - { \left( \sin ( x ) \right) }^{ 4 } } = 2 {\cos(x)}^{2} - 1$
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Answer 1

$lhs \\ \frac{ { \left(1-2 { \left( \sin ( x ) \right) }^{ 2 } \right) }^{ 2 } }{ { \left( \cos ( x ) \right) }^{ 4 } - { \left( \sin ( x ) \right) }^{ 4 } } \\ \frac{ { \cos(2x) }^{2} }{( { \sin(x) }^{2} + { \cos(x) )}^{2} ( { \cos(x) }^{2} - { \sin(x) }^{2} ) } \\ \frac{ { \cos(2x) }^{2} }{ \cos(2x) } \\ \cos(2x) \\ 2 { \cos(x) }^{2} - 1$

hence LHS = RHS