document.write( "Question 580468: find the exact value of cos(sin inverse 1/3 - tan inverse 1/2) \n" ); document.write( "
Algebra.Com's Answer #371286 by lwsshak3(11628)\"\" \"About 
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find the exact value of cos(sin inverse 1/3 - tan inverse 1/2)
\n" ); document.write( "sin^-1 (1/3) and tan^-1 (1/2) are both angles
\n" ); document.write( "use cos addition formula to solve:
\n" ); document.write( "cos(s-t)=cos s cos t + sin s sin t
\n" ); document.write( "s=sin^-1 (1/3)
\n" ); document.write( "sin s=1/3
\n" ); document.write( "cos s=√8/3
\n" ); document.write( "..
\n" ); document.write( "t=tan^-1 (1/2)
\n" ); document.write( "sin t=1/√5
\n" ); document.write( "cos t=2/√5
\n" ); document.write( "cos[sin^-1 (1/3) + tan^-1 (1/2)]
\n" ); document.write( "=√8/3*2/√5+1/3*1/√5
\n" ); document.write( "=2√8/3√5+1/3√5
\n" ); document.write( "=(2√8+1)/(3√5)
\n" ); document.write( "..
\n" ); document.write( "checking answer with calculator:
\n" ); document.write( "sin^-1 (1/3)≈.3398 radians
\n" ); document.write( "tan^-1 (1/2)≈.4636 radians
\n" ); document.write( ".3398-.4636≈-.1238
\n" ); document.write( "cos(-.1238)≈.9923
\n" ); document.write( "..
\n" ); document.write( "(2√8+1)/(3√5)=.9923
\n" ); document.write( " \n" ); document.write( "
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