**Given Information:**

sin(4θ) = cos(4θ)

5θ and 4θ are acute angles

**Solution:**

To find the value of θ, we can use the trigonometric identity:

sin^2θ + cos^2θ = 1

Let's simplify the given equation using this identity.

sin^2(4θ) + cos^2(4θ) = 1

Since sin^2(θ) + cos^2(θ) = 1, we can rewrite the equation as:

sin^2(4θ) + sin^2(π/2 - 4θ) = 1

Applying the trigonometric identity sin^2θ + cos^2θ = 1, we can rewrite the equation as:

sin^2(4θ) + cos^2(π/2 - 4θ) = 1

Since sin^2(θ) + cos^2(θ) = 1, the above equation can be simplified as:

sin^2(4θ) + sin^2(4θ) = 1

2 sin^2(4θ) = 1

Dividing both sides of the equation by 2, we get:

sin^2(4θ) = 1/2

Taking the square root of both sides, we have:

sin(4θ) = ± √(1/2)

Since 5θ and 4θ are acute angles, the value of sin(θ) and cos(θ) will be positive.

Therefore, sin(4θ) = √(1/2)

We know that sin(π/4) = √(1/2), so we can write:

4θ = π/4

Dividing both sides of the equation by 4, we get the value of θ:

θ = π/16

Therefore, the value of θ is π/16.

Sin 5theta=cos4thetacos(90-5theta)=cos 4theta90-5theta= 4theta​90= 5theta+4theta90= 9thetatheta= 90/9theta= 10 degreeHey gayu it's like this