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# Find cos(s+t) and cos(s-t)?

Given : Cos s= -8/17 & cos t=-3/5 & s and t are in quadrant 3

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- Raj KLv 79 years agoFavorite Answer
Find cos(s+t) and cos(s-t)?

Given : Cos s= -8/17 & cos t=-3/5 & s and t are in quadrant 3

Now cos(s) = −8/17

sin(s) =±√ {1−cos²(s)}

=±√ {1−(−8/17)²}=±√ {1−64/289}=±√ {225/289}=±15/17

Rejecting + sign because s is in third quadrant

Hence sin(s)=−15/17

Also cos(t) = −3/5

sin(s) =±√ {1−cos²(s)}

=±√ {1−(−3/5)²}=±√ {1−9/25}=±√ {16/25}=±4/5

Rejecting + sign because t is in third quadrant

Hence sin(t)=−4/5

cos(s+t)=cos(s)cos(t)−sin(s)sin(t)

=(−8/17)×(−3/5)−{(−15/17)×(−4/5)}

=24/85−60/85 = −36/85

Again

cos(s−t)=cos(s)cos(t)+sin(s)sin(t)

=(−8/17)×(−3/5)+{(−15/17)×(−4/5)}

=24/85+60/85 =84/85

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