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without using the calculator

find cos5

khaled yassien












co ED







( )














:
18 18






15 15




22.5 22.5





12 12







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:
(/2) (/2) (/2)
:

> 2 = ( + )
: / = / = /
/ = ( + )/( + ) = 2 /( + )
2 = ( + ) ... ... ... (1)
+ + = 180 > /2 = 90 - ( + )/2
(1)
4 (/2).(/2) = 2*[( + )/2 ]*[( - )/2]
2*(/2)*(/2) = (/2)*[(/2).(/2) + (/2).(/2)]
2 (/2) = [(/2).(/2) + (/2).(/2)]
2 [( + )/2] = [(/2).(/2) + (/2).(/2)]
2*[(/2).(/2) - (/2).(/2)] = [(/2).(/2) + (/2).(/2)]
(/2).(/2) = 3*(/2).(/2)
(/2).(/2)
(/2).(/2) = 3 ... ... ... (2)
(/2) = [( + )/2] = [(/2) + (/2)] [1 - (/2).(/2)]
((/2).(/2))
(/2) = [(/2) + (/2)] [(/2).(/2) - 1]
(2)
(/2) = [(/2) + (/2)] 2
2*(/2) = (/2) + (/2)
:
(/2) (/2) (/2)



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monster

cos(x+x)= cosx-sinx
sin( x+x)= 2sin x *conx







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