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Question

If cos A = 45, cos B = 1213, 3π2<A,B<2π, find the values of the following.
(i) cos (A + B)
(ii) sin (A - B)

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Solution

A and B both lie in the IV quadrant.
=> sinA,sinB are negative

cosA=45=>sinA=35

cosB=1213=>sinB=513

(i) cos(A+B)=cosA.cosBsinA.sinB=45.121335.513=3365

(ii)sin(AB)=sinA.cosBcosA.sinB=35.121345.513=1665

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