Question

1 - cos⁴A answer with solution

Answer 1

= > 1 - cos⁴A


= > 1⁴ - cos⁴A


= > ( 1² ) - ( cos²A )²



$\bold{By \: \: Using \: \: \: ( a )^{2} - ( b )^{2} = ( a + b )( a - b )}$



= > ( 1 - cos²A )( 1 + cos²A )


We know,
sin²A + cos²A = 1
And, sin²A = 1 - cos²A



Substituting the value of 1 - cos²A in solution.



= > ( sin²A )( 1 + cos²A )


= > sin²A( 1 + cos²a )


$\:$



Therefore,1 - cos⁴A = sin²A( 1 + cos²A )

Answer 2

1 - cos⁴A


( 1 )⁴ - cos⁴A


{ ( 1 )² }² - { cos²A }²


{ 1² - cos²A }{ 1² + cos²A ]


{ 1 - cos²A }{ 1 + cos²A }



we know, 1 - cos²A = sin²A



{ sin²A }{ 1 + cos²A }


sin²( 1 + cos²A )


sin²A + sin²Acos²A

$\:$