Question #a5ffa

2 Answers
Jim G.
Jan 1, 2018

#sqrt2/2#

Explanation:

#"using the "color(blue)"addition formulae for cos"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(cos(A+-B)=cosAcosB∓sinAsinB)color(white)(2/2)|)))#

#"here we have the expansion of "cos(A+B)#

#"with "A=21" and "B=24#

#rArrcos21cos24-sin21sin24#

#=cos(21+24)^@#

#=cos45^@#

#=1/sqrt2#

#=1/sqrt2xxsqrt2/sqrt2=sqrt2/2#

turksvids
Jan 1, 2018

#sqrt(2)/2#

Explanation:

Use the sum formula for cosine:

#cos(a+b)=cos(a)cos(b)-sin(a)sin(b)#

So for this problem we have:

#cos(21^circ)cos(24^circ)-sin(21^circ)sin(24^circ) = cos(21^circ+24^circ)#
#=cos(45^circ)#

#cos(45^circ)# is a known value!

#cos(45^circ) = sqrt(2)/2#

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