Question

Can anyone help me with these two questions?

Answer 1

Answer:

if I can read it I will can you repost the pic so we can see

Answer 2

Answer:

14. ½ atan(x/5) − 5x / (50 + 2x²)

15. 12 asin(x/6) + x/3 √(36 − x²)

Step-by-step explanation:

14. x = 5 tan θ

θ/2 − sin(2θ)/4

Use double angle formula:

sin(2θ) = 2 tan θ / (1 + tan² θ)

tan θ = x / 5, so:

sin(2θ) = (2x/5) / (1 + x²/25)

sin(2θ) = 10x / (25 + x²)

Substitute:

θ/2 − (10x / (25 + x²)) / 4

θ/2 − 5x / (50 + 2x²)

½ atan(x/5) − 5x / (50 + 2x²)

15. x = 6 sin θ

12θ + 6 sin 2θ

Use double angle formula:

sin(2θ) = 2 sin θ cos θ

sin(2θ) = 2 sin θ √(1 − sin² θ)

sin θ = x / 6, so:

sin(2θ) = (x/3) √(1 − x²/36)

sin(2θ) = x/18 √(36 − x²)

Substitute:

12θ + 6 (x/18 √(36 − x²))

12θ + x/3 √(36 − x²)

12 asin(x/6) + x/3 √(36 − x²)