Find the exact value of -cos (7pi)/12?

1 Answer
Jim G.
Mar 16, 2018

#1/4(sqrt6-sqrt2)#

Explanation:

#"using the "color(blue)"addition formula for cosine"#

#•color(white)(x)cos(A+B)=cosAcosB-sinAsinB#

#"note that "(7pi)/12=pi/3+pi/4#

#rArrcos((7pi)/12)=cos(pi/3+pi/4)#

#rArr-cos(pi/3+pi/4)#

#=-(cos(pi/3)cos(pi/4)-sin(pi/3)sin(pi/4))#

#=-(1/2xx1/sqrt2-sqrt3/2xx1/sqrt2)#

#=-(1/(2sqrt2)-sqrt3/(2sqrt2))#

#=-((1-sqrt3)/(2sqrt2)xxsqrt2/sqrt2)#

#=-((sqrt2-sqrt6)/4)=1/4(sqrt6-sqrt2)#

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