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find the exact value using a sum or difference identity of cos 105°

Find The Exact Value Using A Sum Or Difference Identity Of Cos 105 class=

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Answer:

Step-by-step explanation:

We can easily determine the exact value of this unknown angle by breaking it into known angles that can add together to give up 105. For example, 105 degrees is 60 + 45, both of which are found on the unit circle. We ill also use the trig identity for the sum of the cos of 2 angles which is:

[tex]cos(60+45)=cos60cos45-sin60sin45[/tex]

These values are found on the units circle, so make sure you have one handy. Those values fill in as follows:

[tex](\frac{1}{2})(\frac{\sqrt{2} }{2})-(\frac{\sqrt{3} }{2})(\frac{\sqrt{2} }{2})[/tex] which simplifies to

[tex]\frac{\sqrt{2}-\sqrt{6} }{4}[/tex]

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