Question

Sin^4a*cos^2a+sin^2a*cos^4a=

Answer 1

Sin^4a*cos^2a+sin^2a*cos^4a = sin^2a*cos^2a*(sin^2a+cos^2a) = sin^2a*cos^2a 

Answer 2

To simplify the expression sin^4(a) * cos^2(a) + sin^2(a) * cos^4(a), we can factor out common terms:

sin^4(a) * cos^2(a) + sin^2(a) * cos^4(a)

= (sin^2(a) * cos^2(a)) * (sin^2(a) + cos^2(a))

Now, recall the trigonometric identity: sin^2(a) + cos^2(a) = 1

Substitute this into the expression:

= (sin^2(a) * cos^2(a)) * 1

= sin^2(a) * cos^2(a)

Now, we can apply another trigonometric identity: sin^2(a) = 1 - cos^2(a)

Substitute this into the expression:

= (1 - cos^2(a)) * cos^2(a)

Expand:

= cos^2(a) - cos^4(a)

So, the simplified form of the expression is:

cos^2(a) - cos^4(a)