Determine the exact value of
c)sin45°÷sec45°
To solve this, we have to understand that secθ is the reciprocal of cosθ. Therefore, sec45° is equal to 1/cos45°.
Since cos45° is equal to 1/√2, sec45° is equal to 1/(1/√2).
To simplify this, we multiply the numerator and denominator by √2:
sec45° = √2/1 = √2.
Now, we can find sin45° ÷ sec45°:
sin45° ÷ sec45° = sin45° / √2.
Since sinθ is equal to 1/√2 at 45°, we can substitute this value:
sin45° ÷ sec45° = (1/√2) / √2.
To simplify this expression, we multiply the numerator and denominator by √2:
sin45° ÷ sec45° = (1/√2) * (√2/√2) = 1/2.
Therefore, the exact value of sin45° ÷ sec45° is 1/2.