SOLUTION: Give the exact value of the following: cos(sin inverse(1/5)+ cos inverse(2/7))

Question 820891: Give the exact value of the following:
cos(sin inverse(1/5)+ cos inverse(2/7))
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Give the exact value of the following:
cos(sin inverse(1/5)+ cos inverse(2/7))
***
let x=angle whose sine=1/5
sinx=1/5
cosx=√(1-sin^2x)=√(1-(1/25))=√(24/25)=√24/5
..
let y=angle whose cos=2/7
cosy=2/7
siny=√(1-cos^2y)=√(1-4/49)=√(45/49)=√45/7
..
cos(sin inverse(1/5)+ cos inverse(2/7))=cos(x+y)
cos(x+y)=cosxcosy-sinxsiny=(√24/5*2/7)-(1/5*√45/7)=(2√24/35)-(√45/35)=(2√24-√45)/35
cos(sin inverse(1/5)+ cos inverse(2/7))=(2√24-√45)/35
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