Determine the exact value of
Sin45°÷sec45°
The value of sin(45°) is √2/2.
The value of sec(45°) is 1/cos(45°). Since cos(45°) also equals √2/2, sec(45°) is equal to 1/(√2/2), or 2/√2.
So sin(45°)/sec(45°) is (√2/2) / (2/√2).
To simplify this, we multiply the numerator and denominator by √2, which gives us (√2 * √2/2) / (2 * √2/√2).
This further simplifies to (2/2) / (2 * √2/√2), or 1 / (2 * √2/√2).
Simplifying the denominator, we have 1 / (2 * 1), or 1/2.
The exact value of sin(45°)/sec(45°) is 1/2.