Question

if sinA = -5%13 ams cos B = -7%25 and A,B lie in third quadrant then sin(A-B)= what ?​

Answer 1

In third quadrant, both sin and cos are negative.
sin A= -5/13 therefore, cos A= -12/13
cos B= -7/25 therefore, sin B= -24/25
Therefore, sin(A-B)=sinA.cosB-cosA.sinB=(-5/13)(-7/25)-(-12/13)(-24/25)=(35-288)/(13*25)=-253/325 (ans)
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Answer 2

sin(A-B) = -5/13*(-7/25) - (-12/13)*(-24/25)
= 35/325- 288/325 = -253/325