Question

Question #b18ed

Answer 1

2

Explanation:

Develop the numerator, after replacing 1 by (sin^2 x + cos^2 x) -->
`N = sin^2 x + cos ^2 x - sin^4 x - cos^4 x =`
`= sin^2 x(1 - sin ^2 x) + cos ^2 x (1 - cos^2 x) =`
Use trig identities
`1 - sin^2 x = cos^2 x`
`1 - cos^2 x = sin^2 x`
`N = sin^2 x.cos^2 x + cos^2 x.sin^2 x`
Denominator:`D = sin^2 x.cos^2 x`
The expression becomes:
`E = N/D = 1 + 1 = 2`

Answer 2

`( 1-(sin^4x+cos^4x ))/ (cos^2xsin^2x)`

`=( 1-((sin^2x+cos^2x )^2-2sin^2xcos^2x))/ (cos^2xsin^2x)`

`=( 1-(1^2-2sin^2xcos^2x))/ (cos^2xsin^2x)`

`=( 1-1+2sin^2xcos^2x)/ (cos^2xsin^2x)`

`=(2sin^2xcos^2x)/ (cos^2xsin^2x)=2`