Find tan(A + B) given that cos A = -5/13 , with A in quadrant II, and with sinB =8/17 in quadrant II

Answer 1

Greetings! Lets solve this shall we ?

So, given cosA = -5/13 and sinB = 8/17, we must find tan(A+B) which is an Addition Identity on the list of identities.

If cosA = -5/13, then Pythagorean Theorem says x² + (-5)² = (13)² | x² + 25 = 169 | x² = 144 | x = 12. Now, sinA = 12/13 such that tanA = -12/5.

If sinB = 8/17, then Pythagorean Theorem says x² +(8)² = (17)² | x² + 64 = 289| x² = 225| x = 15. Now, cosB = 15/17 such that tanB = 8/15.

Let tan(A+B) = (tanA + tanB) / (1-tanAtanB) = (-12/5 + 8/15) / (1+(96/75)) = (-28/15) / (171/75) = (-28/15)*(75/171) = -140/171.

I hope this helped!