Penjelasan dengan langkah-langkah:

To simplify this expression, we can use the identity sin^2(x) + cos^2(x) = 1:

sin^2(35) + cos^2(160) + sin^2(55) + cos^2(70)

= 1 + cos^2(160) + 1 + cos^2(70)

= 2 + cos^2(160) + cos^2(70)

Now we can use the identity cos(2x) = 2cos^2(x) - 1 to rewrite the expression in terms of cos(2x):

= 2 + 2cos^2(80) - 1 + 2cos^2(35) - 1

= 3 + 2cos^2(80) + 2cos^2(35) - 2

= 3 + cos(160) + cos(70) - 2

Finally, we can use the identity cos(x+y) = cos(x)cos(y) - sin(x)sin(y) to simplify the expression further:

= 3 + (cos(80)cos(80) - sin(80)sin(80)) + (cos(35)cos(35) - sin(35)sin(35)) - 2

= 3 + cos(160) + cos(70) - 2

= 3 - cos(160) - cos(70) - 2

= -cos(160) - cos(70) - 1

So the value of the expression is -cos(160) - cos(70) - 1.