Question

Cos 5pi/12-cos pi/12

Answer 1

Ответ на картинке внизу

Answer 2

To calculate the value of cos(5π/12) - cos(π/12), we can use the formula for the difference of cosines:

cos(a) - cos(b) = -2sin((a + b)/2)sin((a - b)/2)

In this case, a = 5π/12 and b = π/12. Let's substitute these values into the formula:

cos(5π/12) - cos(π/12) = -2sin((5π/12 + π/12)/2)sin((5π/12 - π/12)/2)

Simplifying the fractions inside the sine functions:

cos(5π/12) - cos(π/12) = -2sin(6π/24)sin(4π/24)

Further simplification:

cos(5π/12) - cos(π/12) = -2sin(π/4)sin(π/6)

The sine values for π/4 and π/6 are √2/2 and 1/2, respectively:

cos(5π/12) - cos(π/12) = -2 * (√2/2) * (1/2)

Finally, simplifying the expression:

cos(5π/12) - cos(π/12) = -√2/2

Therefore, cos(5π/12) - cos(π/12) equals -√2/2.