Step-by-step explanation:
sin⁴A + sin²Acos²A = sin²A
<u>Proving the left hand side ( LHS)</u>
That's
sin⁴A can be written as ( sin²A)(sin ²A)
So we have
( sin²A)(sin ²A) + sin²Acos²A
<u>Next factor sin²A out</u>
That's
sin²A ( sin²A + cos²A)
Using trigonometric identities
That's
<h3>sin²A + cos²A = 1</h3>
<u>Simplify the expression</u>
That's
sin²A × 1
We have the final answer as
<h2>sin²A</h2>
As proven
Hope this helps you