Determine the exact value of
b) sin45°*sec45°
To determine the exact value of sin 45° * sec 45°, we first need to find the values of sin 45° and sec 45° separately.
sin 45° can be found using the Pythagorean identity: sin^2 θ + cos^2 θ = 1.
Since cos 45° is equal to sin 45° (as cos 45° = √(2)/2), we have:
sin^2 45° + (sin 45°)^2 = 1
2(sin 45°)^2 = 1
(sin 45°)^2 = 1/2
sin 45° = √(1/2) = √2/2
sec 45° can be found using the reciprocal identity: sec θ = 1/cos θ.
Since cos 45° = √(2)/2, we can find sec 45° as:
sec 45° = 1/(√(2)/2) = 2/√2 = √2
Therefore, sin 45° * sec 45° = (√2/2) * √2.
Multiplying the numerators (√2 * √2) and the denominators (2 * 1), we get:
= 2/2 = 1.
Therefore, sin 45° * sec 45° = 1.