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:

Question

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)

Philoid · Accepted Answer

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

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)

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)