Question

cos⁴A + sin⁴A - 2sin²A.cos²A = (2cos²A-1)²​

Answer 1

Answer:

${ \cos }^{4} \alpha + { \sin }^{4} \alpha - 2 { \sin }^{2} \alpha . { \cos }^{2} \alpha = (2 { \cos}^{2} \alpha - 1) ^{2} \\ > ({ \cos }^{2} \alpha )^{2} + { ({ \sin }^{2} \alpha })^{2} - 2. \sin^{2} \alpha . { \cos}^{2} \alpha = (2 { \cos }^{2} \alpha - 1) ^{2} \\ > ( { \cos}^{2} \alpha - { \sin}^{2} \alpha ) ^{2} = ( 2{ \cos }^{2} - 1) ^{2} \\ > { \cos }^{2} \alpha - { \sin }^{2} \alpha = 2 { \cos }^{2} \alpha - 1 \\ > 2 { \cos }^{2} \alpha - { \cos}^{2} \alpha = 1 - { \sin }^{2} \alpha \\ > { \cos }^{2} \alpha = 1 - { \sin }^{2} \alpha \\ > \sin^{2} \alpha + { \cos}^{2} \alpha = 1$