Question

If sin(15 ∘) = 1/2√a-b​ , what are the values of a and b?

A) a=3,b=2
B) a=2,b=3
C) a=5,b=4
D) a=4,b=5

Answer 1

sin(15°) is √(2 - √3)/2. By setting 1/(2√(a-b)) equal to this value and solving, we find that a = 4 and b = 5.

Step-by-step explanation:

The question asks about finding the values of a and b given that sin(15°) = 1/(2√(a-b)). First, it's important to know the exact value of sin(15°). We can use the half-angle formula: sin(±°) = √((1 - cos(2±°))/2), or in this case sin(15°) = √((1 - cos(30°))/2).

sin(15°) is √(2 - √3)/2. By setting 1/(2√(a-b)) equal to this value and solving, we find that a = 4 and b = 5

Knowing that cos(30°) = √3/2, we find that sin(15°) = √((1 - √3/2)/2), which simplifies to sin(15°) = √(2 - √3)/2. This means that 1/(2√(a-b)) should be equal to √(2 - √3)/2. By cross-multiplying and squaring both sides, we get a = 4 and b = 5. Therefore, the values of a and b are 4 and 5 respectively.