Question 998441
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Find the exact value of cos 75 degree
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First,  cos(75°) = sin(15°)     (the reduction formula).


Next,  sin(15°) = {{{sin((30^0)/2)}}} = {{{sqrt(1-cos(30^0))/2)}}} =       (formula of half-argument for sine) = 

= {{{sqrt((1-sqrt(3)/2)/2)}}} = {{{sqrt((2-sqrt(3))/4)}}} = {{{sqrt(2-sqrt(3))/2}}}.


<U>Answer</U>. &nbsp;cos(75°) = {{{sqrt(2-sqrt(3))/2}}}.


See the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometric-functions-of-half-argument.lesson>Trigonometric functions of half argument</A> &nbsp;and 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometric-functions-of-half-argument-Examples.lesson>Trigonometric functions of half argument - Examples</A>

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