Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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°)

Given That Tan A 512 And Tan B 43 Such That A Is An Acute Angle And B Is An Obtuse Angle Find The Value Ofa Tan A45b Tan B360 class=

Sagot :

Solve for tan(A-45°).

Recall that tan(45°) = 1

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

Therefore, tan(A-45°) = -7/17.

Solve for tan(B+360°)

Recall that tan(360°) = 0

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

Therefore, tan(B+360°) = 5/7.

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.