If cosA = –12/13 and cotB = 24/7, where A lies in the second quadrant and B in the third quadrant, find the values of the following:

(i) sin(A +B) (ii) cos(A +B) (iii) tan(A +B)


Given cosA = -12/13 And cotB = 24/7


A lies in second quadrant And B in the third quadrant.


The sine function is positive in the second quadrant and in the third quadrant,Both sine And cosine functions are negative.


We know that







Now,


(i) Sin(A +B)


We know that sin(A +B) = sinA cosB + cosA sinB





(ii) Cos(A +B)


We know that cos(A +B) = cosA cosB - sinA sinB





(iii) Tan(A +B)


We know that




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