Question

Cos⁴A -Sin ⁴ A tell me with explanation the final answer is 2cos²A -1​

Answer 1

cos^4x.-sin^4x = (cos^2x+sin^2x)(cos^2x-sin^2x)

=1(cos^2x-sin^2x)

=cos2a (identity)

= 2cos^x-1

Answer 2

Solution:-

=> Cos⁴A - Sin⁴A

we can write it as

=> (Cos²A)² - (Sin²A)²

{ from a² - b² = ( a + b ) ( a - b ) }

=> (Cos²A + Sin²A) (Cos²A - Sin²A)

{ from Cos²A + Sin²A = 1 }

=> 1 (Cos²A - Sin²A)

{ from Sin²A = 1 - Cos²A }

=> 1 ( Cos²A - [ 1 - Cos² A ] )

=> Cos² A - 1 + Cos² A

=> 2Cos²A - 1