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Answer:
[tex]\tan(A - \frac{\pi}{4}) = \frac{-\sqrt{15}- 1}{1 -\sqrt{15}}[/tex]
Step-by-step explanation:
Given
[tex]\tan A =-\sqrt{15[/tex]
Required
Find [tex]\tan(A - \frac{\pi}{4})[/tex]
In trigonometry:
[tex]\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}[/tex]
This gives:
[tex]\tan(A - \frac{\pi}{4}) = \frac{\tan A - \tan \frac{\pi}{4}}{1 + \tan A \tan \frac{\pi}{4}}[/tex]
[tex]tan \frac{\pi}{4} = 1[/tex]
So:
[tex]\tan(A - \frac{\pi}{4}) = \frac{\tan A - 1}{1 + \tan A * 1}[/tex]
[tex]\tan(A - \frac{\pi}{4}) = \frac{\tan A - 1}{1 + \tan A}[/tex]
This gives:
[tex]\tan(A - \frac{\pi}{4}) = \frac{-\sqrt{15}- 1}{1 -\sqrt{15}}[/tex]
Answer:
StartFraction StartRoot 15 EndRoot + 1 Over 1 minus StartRoot 15 EndRoot EndFraction
Step-by-step explanation:
EndRoot EndFraction StartFraction negative StartRoot 15 EndRoot + 1 Over 1 + StartRoot 15 EndRoot EndFraction