Question

(sin^4a+cos^4a)-6sin^2acos^2a=cos4a

Answer 1

Sin^4 a +Cos^4 a -2Sin^2 aCos^2 a -4Sin^2 aCos^2 a =
 =(Cos^2 a - Sin^2 a)^2 - Sin^2 2aCos^2 2a - Sin^2 2a = Cos 4a

Answer 2

To solve the equation (sin^4a + cos^4a) - 6sin^2a * cos^2a = cos4a, we'll work on simplifying the left side and then compare it to the right side.

1. Start by expanding sin^4a and cos^4a: (sin^2a)^2 + (cos^2a)^2 - 6sin^2a * cos^2a = cos4a

2. Simplify: (sin^2a + cos^2a)^2 - 6sin^2a * cos^2a = cos4a

3. Use the trigonometric identity sin^2a + cos^2a = 1: 1^2 - 6sin^2a * cos^2a = cos4a

4. Simplify: 1 - 6sin^2a * cos^2a = cos4a

Now we can compare the left side (1 - 6sin^2a * cos^2a) to the right side (cos4a) to check if the equation holds true for all values of 'a'.

If the equation holds true for all values of 'a', then we can conclude that the original equation is true.