Question

Answer this fast plz....

Answer 1

Hi ,

take numerator ,

a ) cos² x + sin⁴ x

= cos² x + ( sin² x )²

= cos² x + ( 1 - cos² x ) ²

= cos² x + 1 - 2cos²x + cos⁴ x

= 1 - cos² x + cos⁴ x ----( 1 )

b ) take denominator ,

sin² x + cos⁴ x

= 1 - cos² x + cos⁴ x ---( 2 )

we observe that ,

( 1 ) = ( 2 )

now , substitute ( 1 ) and ( 2 ) I'm

given f ( x ) ,


f( x ) = ( cos²x + sin⁴ x ) / ( sin² x + cos⁴ x )

= ( 1 ) / ( 2 )

= 1

Therefore ,

f ( 2012 ) = 1

I hope this helps you.

: )

Answer 2

$Given : \frac{cos^2x + sin^4x}{sin^2x + cos^4x}$

$\frac{(1 - sin^2x) + sin^4x}{sin^2x + (1 - sin^2x)^2}$

$\frac{1 - sin^2x + sin^4x}{sin^2x + 1 + sin^4x - 2sin^2x}$

$\frac{1 - sin^2x + sin^4x}{1 - sin^2x + sin^4x}$

1.


Therefore f(2012) = 1.


Hope this helps!