cos(115)-cos(15)

[courteous]

Calculate exactly as a rational fraction (that is, w/o calculator) $\displaystyle \cos115-\cos15$. (The answer is $\displaystyle -\frac{\sqrt6}{2}$.)

$\displaystyle =-cos65-cos15=-sin25-cos15=$... :?:

 

[arthur ohlsten]

there appears to be a error in the problem
cos 115=-.4226
cos15=.9659
cos115-cos15=-1.3885

-[square root 6] /2= -1.2247

thus cos115-cos15 does not equal 6^1/2 /2 answer

Arthur

 

[Deleted member 4993]

Calculate exactly as a rational fraction (that is, w/o calculator) $\displaystyle \cos115-\cos15$. (The answer is $\displaystyle -\frac{\sqrt6}{2}$.)

I think you have

cos(105°) - cos (15°)

= cos(60°+45°) - cos(60° - 45°)

Now continue....
$\displaystyle =-cos65-cos15=-sin25-cos15=$... :?:

 

[courteous]

there appears to be a error in the problem

You are right, there is an error in the problem. An error being me! The first time I've read $\displaystyle 115$ and then confirmation bias kicked in. It is written as Subhotosh guessed ( :shock: ): $\displaystyle \cos105-\cos15$

I think you have

cos(105°) - cos (15°)

= cos(60°+45°) - cos(60° - 45°)

Now continue....

Subhotosh, thank you, I couldn't have solved it without $\displaystyle cos(60 - 45)$. Wondering though if there are more ways to solve it :?: