document.write( "Question 795486: Let α & β be acute angles such that tan α=7 and sin β=4/5. Prove that α+β = 3/4π\r
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Let α & β be acute angles such that tan α=7 and sin β=4/5. Prove that α+β = 3/4π
\n" ); document.write( "Hint: Consider cos(α+β)
\n" ); document.write( "***
\n" ); document.write( "Identity: tan(a+b)=(tan(a)+tan(b))/1-tan(a)*tan(b)
\n" ); document.write( "tan(a)=7
\n" ); document.write( "sin(b)=4/5 (3-4-5 right triangle)
\n" ); document.write( "cos(b)=3/5
\n" ); document.write( "tan(b)=sin(b)/cos(b)=4/3
\n" ); document.write( "tan(a+b)=((7+(4/3))/1-7*4/3
\n" ); document.write( "=(25/3)/1-(28/3)
\n" ); document.write( "=(25/3)/-(25/3)
\n" ); document.write( "=-1
\n" ); document.write( "tan(a+b)=-1
\n" ); document.write( "(a+b)=3π/4 (in quadrant II where tan<0) \n" ); document.write( "

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