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 :?: