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If csc A= -5/3 and csc B = -13/5 with angle A and angle B in quadrant 3. What is value of cos(A-B)?

1 Answer

Jul 23, 2016

#cos(A-B)=63/65#.

Explanation:

We start by taking note that angles #A and B# are in #Q_(III#, so that, #cosA and cosB# both will be #-ve#.

#cscA=-5/3rArrsinA=-3/5rArrcosA=-sqrt(1-sin^2A)=-sqrt(1-9/25)=-sqrt16/25=-4/5#

Similarly, #cscB=-13/5rArrcosB=-12/13#

Therefore, reqd. value#=cos(A-B)=cosAcosB+sinAsinB#

#=(-4/5)(-12/13)+(-3/5)(-5/13)#

#48/65+15/65=63/65#.

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