Question 1114896
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Given: cos (-105)
Find the exact value of the function without the use of a calculator.

I was unsure what to do with a negative, but from examples, I did the following where it "ignores" the negative.

cos (105) = cos (135 - 30) 
{{{ cos (135) cos (30) + sin (135) sin (30) }}}
{{{ (-sqrt(2)/2)(sqrt(3)/2) + (sqrt(2)/2)(1/2) }}}
{{{ (-sqrt(6)/4)+ (sqrt(2)/4) }}}
Final Answer: {{{ (sqrt(2)-sqrt(6)) / (4) }}}
If the final answer is right, why does the (-) go away and if that procedure is incorrect how would you split up
the -105? Thank you for any help! 
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You're applying the DIFFERENCE of 2 angles here, which does give you 
{{{(-sqrt(6)/4)+ (sqrt(2)/4)}}}. However, the NEGATIVE is NOT IGNORED/does NOT just DISAPPEAR.

{{{(-sqrt(6)/4)+ (sqrt(2)/4)}}} <==== You got up to this point
{{{((- sqrt(6) + sqrt(2))/4)}}}, which is EQUAL to, or the SAME as:  {{{((sqrt(2) - sqrt(6))/4)}}}. 
YOUR Final Answer: {{{(sqrt(2) - sqrt(6))/(4)}}}
Looking at the 2 expressions ABOVE, one can clearly see that they're the SAME.

<font color = red><font size = 4><b><u>**Note:</font></font></b></u>
You asked how the cos (- 105) could be SPLIT, if your answer is incorrect. Your answer isn't incorrect, as stated 
above, but another SPLIT would be cos (- 105) = cos (- 60 - 45), or {cos [(- 60) + (- 45)]}, which would then
involve the SUM of 2 angles. Nonetheless, this yields the same result!</pre>