Question

Find \cos\left(\dfrac{13\pi}{12}\right)cos( 12 13π ​ )cosine, (, start fraction, 13, pi, divided by, 12, end fraction, )exactly using an angle addition or subtraction formula.

Answer 1

To find cos(13π/12) using an angle addition or subtraction formula, we can rewrite 13π/12 as the sum or difference of angles with known cosines and sines. Using the formula cos(a+b) = cos(a)cos(b) - sin(a)sin(b), we can substitute the values and simplify to find that cos(13π/12) = √3/2.

Step-by-step explanation:

To find cos(13π/12) using an angle addition or subtraction formula, we can use the formula cos(a+b) = cos(a)cos(b) - sin(a)sin(b).

First, we need to express 13π/12 as the sum or difference of angles whose cosines we know.

Since 13π/12 is not a standard angle measure, we can rewrite it as 12π/12 + π/12.

The cosine of 12π/12 is 1 and the cosine of π/12 is √3/2. Next, the sine of 12π/12 is 0 and the sine of π/12 is 1/2.

Substituting these values into the formula, we have cos(13π/12) = cos(12π/12)cos(π/12) - sin(12π/12)sin(π/12) = (1)(√3/2) - (0)(1/2) = √3/2.

Answer 2

Step-by-step explanation:

`cos((13\pi )/(12) )\\=cos(\pi +(\pi )/(12) )\\=-cos((\pi )/(12) )\\=-cos((\pi )/(3) -(\pi )/(4) )\\=-[cos (\pi )/(3) cos(\pi )/(4) +sin(\pi )/(3) sin(\pi )/(4) ]\\=-[(1)/(2) *(1)/(√(2) ) +(√(3) )/(2) *(1)/(√(2) ) ]\\=-(1+√(3) )/(2√(2) )`