Question

Sin^2x-sin^4x+cos^4x=

Answer 1

Sin^2x(1-sin^2x)+cos^4x = sin^2x*cos^2x+cos^4x =cos^2x(sin^2x+cos^2x) = cos^2x

Answer 2

To simplify the expression sin^2(x) - sin^4(x) + cos^4(x), we can use the trigonometric identity sin^2(x) + cos^2(x) = 1. Rearranging this identity, we get sin^2(x) = 1 - cos^2(x).

Substituting this into the original expression, we have:

sin^2(x) - sin^4(x) + cos^4(x) = (1 - cos^2(x)) - sin^4(x) + cos^4(x).

Expanding and rearranging terms, we get:

= 1 - cos^2(x) - sin^4(x) + cos^4(x) = 1 - sin^4(x) - cos^2(x) + cos^4(x).

Now, let's focus on the terms involving sin(x) raised to a power. We can use the identity cos^2(x) = 1 - sin^2(x) to substitute for cos^2(x):

= 1 - sin^4(x) - (1 - sin^2(x)) + cos^4(x) = 1 - sin^4(x) - 1 + sin^2(x) + cos^4(x) = -sin^4(x) + sin^2(x) + cos^4(x).

Finally, combining like terms, we have the simplified expression:

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

Therefore, the simplified form of the expression is -sin^4(x) + sin^2(x) + cos^4(x).