If sin^4A - cos^4A = 1 ,then find the value of A/2.

Plzz give the answer soon

We are given:

sin⁴A - cos⁴A = 1

Step 1: Use the identity for difference of squares
The given expression can be simplified using the identity:

a² - b² = (a - b)(a + b)

Here, let:

a = sin²A
b = cos²A

Now,

sin⁴A - cos⁴A = (sin²A - cos²A)(sin²A + cos²A)

Since sin²A + cos²A = 1 (from the Pythagorean identity),

sin⁴A - cos⁴A = (sin²A - cos²A)(1)
=> sin⁴A - cos⁴A = sin²A - cos²A

Step 2: Solve for sin²A - cos²A
Given that sin⁴A - cos⁴A = 1,

sin²A - cos²A = 1

From the identity,

sin²A - cos²A = cos(2A)

So,

cos(2A) = 1

Step 3: Find the value of A
cos(2A) = 1 occurs when:

2A = 0°, 360°, 720°, ...
=> A = 0°, 180°, 360°, ...

Step 4: Find A/2
From the possible values of A,

If A = 0°, A/2 = 0°
If A = 180°, A/2 = 90°
If A = 360°, A/2 = 180°

Thus, the possible values of A/2 are 0°, 90°, 180°, ...