SOLUTION: find the exact value of:
cos ( tan^-1 (4/3) + cos^-1 (12/13 ) )
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Question 575074: find the exact value of:
cos ( tan^-1 (4/3) + cos^-1 (12/13 ) )
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
ind the exact value of:
cos ( tan^-1 (4/3) + cos^-1 (12/13 ) )
**
Addition formula for cosine:
cos(x+y)=cos(x)cos(y)-sin(x)sin(y)
..
let x = tan^-1 (4/3) (an angle)
cos(x)=3/5
sin(x)=4/5
..
let y = cos^-1 (12/13) (an angle)
cos(y)=12/13
sin(y)=5/13
..
cos(x+y)=(3/5*12/13)-(4/5*5/13)
cos(x+y)=(36/65)-(20/65)
cos(x+y)=16/65
..
ans:
cos ( tan^-1 (4/3) + cos^-1 (12/13 ) )=16/65
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