SOLUTION: Find the exact value of tan (a-b) if sin a= 4/5 and cos b = 5/13
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Question 1040805: Find the exact value of tan (a-b) if sin a= 4/5 and cos b = 5/13
Firecrazed13@yahoo.com
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ \frac{4}{5})
\ =\ \frac{16}{25})
\ =\ \frac{16}{25})
\ =\ \frac{9}{25})
\ =\ \pm\frac{3}{5})
Similarly, you can show that \ =\ \pm\frac{12}{13})
Therefore
\ =\ \pm\frac{4/5}{3/5}\ =\ \pm\frac{4}{3})
Similarly,
\ =\ \pm\frac{12}{5})
Tangent of the difference formula:
\ =\ \frac{\tan(a)\ -\ \tan(b)}{1\ +\ \tan(a)\tan(b)})
Case 1: \ >\ 0,\ \tan(b)\ >\ 0)
\ =\ \frac{\frac{4}{3}\ -\ \frac{12}{5}}{1\ +\ \left(\frac{4}{3}\right)\left(\frac{12}{5}\right)})
Just do the arithmetic. Then plug in the numbers and do the arithmetic for the other three cases.
John
My calculator said it, I believe it, that settles it
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