☆ The relation between x and y is y = a cos x° +b
Taking 1st condition from the table .
→ x = 0 and y = 9
→ y = a + cos 0° + b
→ 9 = a + cos 0° + b
☆ We know that cos 0° = 1
→ 9 = a(1) + b
→ a + b = 9. equation 1st
Now taking other condition
→ x = 90° and y = 1
→ y = a cos 90° + b
→ 1 = a cos 90° + b
☆ We know that cos 90° is 0
→ 1 = a(0) + b
→ 1 = b
Putting the value of b in equation 1st .
→ 9 = a + 1
→ a = 8 .
Now taking the value of x according to the question .
☆ x = 45 °
→ y = 8 ( cos 45°) + 1
☆ We know that cos 45° is 1/√2
→ y = 8(1/√2) + 1
→ 8 = 4×√2×√2
y = 4√2 +1
So the answer is 4√2+1