Answer:
√3/2
Explanation:
Easy Method
The equation above is in the forms of sin(a)cos(b) - cos(a)sin(b), which is sin(a-b) according to the trig identities. sin(75-15) = sin(60) = √3/2
Harder Method
Find sin75 with equation sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
sin75°
= sin(45° + 30°)
= [sin45°cos30° + cos45°sin30°]
= [√2/2 * √3/2 + √2/2 * 1/2] <-- unit circle known values
= [(√6 + √2)/4]
Find cos75 with the equation: cos(a+b) = sin(a)sin(b) - cos(a)cos(b)
cos75°
= cos(45° + 30°)
= [cos45°cos30° - sin45°sin30°]
= [√2/2 * √3/2 - √2/2 * 1/2] <-- unit circle known values
= [(√6 - √2)/4]
Find sin15 with the equation: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)
sin15°
= sin(45° - 30°)
= [sin45°cos30° - cos45°sin30°]
= [√2/2 * √3/2 - √2/2 * 1/2] <-- unit circle known values
= [(√6 - √2)/4]
Find cos15 with the equation: cos(a-b) = sin(a)sin(b) + cos(a)cos(b)
cos15°
= cos(45° - 30°)
= [cos45°cos30° + sin45°sin30°]
= [√2/2 * √3/2 + √2/2 * 1/2] <-- unit circle known values
= [(√6 + √2)/4]
Now plug in all the solved values, we get: {[(√6 + √2)/4] * [(√6 + √2)/4]} - {[(√6 - √2)/4] * [(√6 - √2)/4]} = √3/2