Question

Sin^4 L-cos^4L+2cos^2L

Answer 1

Держи.............ю.....

Answer 2

Sin⁴@-cos⁴@+2cos²@=(sin²@+cos²@)(sin²@-cos²@)+2cos²@=sin²@-cos²@+2cos²@=sin²@+cos²@=1

Answer 3

To simplify the expression sin^4(L) - cos^4(L) + 2cos^2(L), we'll use trigonometric identities. The identity we'll utilize is:

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

Now, we can rewrite the expression as follows:

sin^4(L) - cos^4(L) + 2cos^2(L)

Since sin^2(L) = 1 - cos^2(L) (using the identity above), we can substitute sin^4(L) with (1 - cos^2(L))^2:

(1 - cos^2(L))^2 - cos^4(L) + 2cos^2(L)

Next, expand the squared term:

(1 - 2cos^2(L) + cos^4(L)) - cos^4(L) + 2cos^2(L)

Now, let's combine like terms:

1 - 2cos^2(L) + cos^4(L) - cos^4(L) + 2cos^2(L)

The two middle terms, cos^4(L) and -cos^4(L), cancel each other out:

1 - 2cos^2(L) + 2cos^2(L)

Finally, the remaining terms also cancel out:

1

So, the simplified expression is 1.