document.write( "Question 745825: If α and β are acute angles such that csc (α) = 17/15 and cot (β) = 3/4, find the following.\r
\n" ); document.write( "\n" ); document.write( "a. sin(α+β)\r
\n" ); document.write( "\n" ); document.write( "b.tan(α+β) \n" ); document.write( "

Algebra.Com's Answer #454030 by lwsshak3(11628) $\"\"$ $\"About$

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If α and β are acute angles such that csc (α) = 17/15 and cot (β) = 3/4, find the following.
\n" ); document.write( "a. sin(α+β)
\n" ); document.write( "b.tan(α+β)
\n" ); document.write( "***
\n" ); document.write( "use a & b for (α & β
\n" ); document.write( "csc(a)=17/15
\n" ); document.write( "sin(a)=15/17
\n" ); document.write( " $\"cos%28a%29=sqrt%281-sin%5E2%28a%29%29=sqrt%281-%28225%2F289%29%29=sqrt%2864%2F289%29=8%2F17\"$
\n" ); document.write( " $\"tan%28a%29=sin%28a%29%2Fcos%28a%29=%2815%2F17%29%2F%288%2F17%29=15%2F8\"$
\n" ); document.write( "...
\n" ); document.write( "cot(b)=3/4
\n" ); document.write( "tan(b)=4/3
\n" ); document.write( "opposite side=4
\n" ); document.write( "adjacent side=3
\n" ); document.write( "hypotenuse=5
\n" ); document.write( "sin(b)=4/5
\n" ); document.write( "cos(b)=3/5
\n" ); document.write( "..
\n" ); document.write( "sin(a+b)=sin(a)cos(b)+cos(a)sin(b)=(15/17)(3/5)+(8/17)(4/5)=(45/85)+(32/85)=77/85
\n" ); document.write( "tan(a+b)=(tan(a)+tan(b))/(1-tan(a)*tan(b))
\n" ); document.write( "=[(15/8)+(4/3)]/[1-(15/8)(4/3)]
\n" ); document.write( "=[45/24+32/24]/[1-60/24]=77/24/-36/24=-77/36
\n" ); document.write( "..
\n" ); document.write( "Check with calculator:
\n" ); document.write( "sin(a)=17/15
\n" ); document.write( "a≈61.9275º
\n" ); document.write( "tan(b)=4/3
\n" ); document.write( "b≈53.1301
\n" ); document.write( "a+b=115.0526
\n" ); document.write( "sin(a+b)=sin(115.0526)≈0.9059
\n" ); document.write( "exact ans=77/85≈0.9059
\n" ); document.write( "tan(a+b)=tan(115.0526)=-2.139..
\n" ); document.write( "exact ans=-77/36≈-2.139.. \n" ); document.write( "

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