SOLUTION: Find the exact value of the expression whenever it is defined. (If an answer is undefined, enter UNDEFINED.) (a) sin [2 arccos (−8/17)] (b) cos (2 sin^−1 7/25)

Question 929015: Find the exact value of the expression whenever it is defined. (If an answer is undefined, enter UNDEFINED.)
(a) sin [2 arccos (−8/17)]
(b) cos (2 sin^−1 7/25)
(c) tan (2 tan^−1 3/5)

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the exact value of the expression whenever it is defined. (If an answer is undefined, enter UNDEFINED.)
(a) sin [2 arccos (−8/17)]
cosx=-8/17
sinx=√(1-(8/17)^2)=√(1-64/289)=√(225/289)=15/17
sin2x=2sinxcosx=2*15/17*-8/17=-240/289
sin [2 arccos (−8/17)]=-240/289
..
(b) cos (2 sin^−1 7/25)
sinx=7/25
cos2x=1-2sin^2(x)=1-2*49/625=1-98/625=527/625
cos (2 sin^−1 7/25)=527/625
..
(c) tan (2 tan^−1 3/5)
tanx=3/5
tan2x=(2tanx)/(1-tan^2(x))=6/5/(1-9/25)=30/25/16/25=30/16
tan (2 tan^−1 3/5)=30/16
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SOLUTION: Find the exact value of the expression whenever it is defined. (If an answer is undefined, enter UNDEFINED.) (a) sin [2 arccos (&#8722;8/17)] (b) cos (2 sin^&#8722;1 7/25)

SOLUTION: Find the exact value of the expression whenever it is defined. (If an answer is undefined, enter UNDEFINED.) (a) sin [2 arccos (−8/17)] (b) cos (2 sin^−1 7/25)