Question

Given that tan A= 5/12 and tan B= -4/3 such that A is an acute angle and B is an obtuse angle find the value of,a) tan (A-45°)b) tan (B+360°)

Answer 1

Solve for tan(A-45°).

Recall that tan(45°) = 1

`\begin{gathered} \tan (A-45\degree)=(\tan A-\tan B)/(1+\tan A\tan B) \\ \tan (A-45\degree)=((5)/(12)-1)/(1+((5)/(12))(1)) \\ \tan (A-45\degree)=(-(7)/(12))/(1+(5)/(12)) \\ \tan (A-45\degree)=(-(7)/(12))/((17)/(12)) \\ \tan (A-45\degree)=-(7)/(17) \end{gathered}`

Therefore, tan(A-45°) = -7/17.

Solve for tan(B+360°)

Recall that tan(360°) = 0

`\begin{gathered} \tan (B+360\degree)=(\tan A+\tan B)/(1-\tan A\tan B) \\ \tan (B+360\degree)=((5)/(12)+0)/(1-((5)/(12))(0)) \\ \tan (B+360\degree)=((5)/(12))/(1-(5)/(12)) \\ \tan (B+360\degree)=((5)/(12))/((7)/(12)) \\ \tan (B+360\degree)=(5)/(7) \end{gathered}`

Therefore, tan(B+360°) = 5/7.