SOLUTION: Write the given expression in terms of x and y only. Simplify the result.
tan(sin^-1x + cos^-1y)
Algebra.Com
Question 711954: Write the given expression in terms of x and y only. Simplify the result.
tan(sin^-1x + cos^-1y)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write the given expression in terms of x and y only. Simplify the result.
tan(sin^-1x + cos^-1y)
notation:
O=opposite side
A=adjacent side
H=hypotenuse
..
let angle a=sin^-1x
sin a=x/1=0/H
O=x, H=1
A=(√(H^2-O^2)=√(1-x^2)
tan a=O/A=x/√(1-x^2)
..
let angle b=cos^-1y
cos b=y/1=A/H
A=y, H=1
O=(√(H^2-A^2)=√(1-y^2)
tan b=O/A=√(1-y^2)/y
..
Identity:
tan(a+b)=(tan a+tan b)/(1-tan a*tan b)
=(x/√(1-x^2)+√(1-y^2)/y)/(1-x/√(1-x^2)*√(1-y^2)/y)
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