You can put this solution on YOUR website! find the exact value of cos(sin inverse 1/3 - tan inverse 1/2)
sin^-1 (1/3) and tan^-1 (1/2) are both angles
use cos addition formula to solve:
cos(s-t)=cos s cos t + sin s sin t
s=sin^-1 (1/3)
sin s=1/3
cos s=√8/3
..
t=tan^-1 (1/2)
sin t=1/√5
cos t=2/√5
cos[sin^-1 (1/3) + tan^-1 (1/2)]
=√8/3*2/√5+1/3*1/√5
=2√8/3√5+1/3√5
=(2√8+1)/(3√5)
..
checking answer with calculator:
sin^-1 (1/3)≈.3398 radians
tan^-1 (1/2)≈.4636 radians
.3398-.4636≈-.1238
cos(-.1238)≈.9923
..
(2√8+1)/(3√5)=.9923
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