Question

Given: tangent A = negative StartRoot 15 EndRoot What is the value of Tangent (A minus StartFraction pi over 4 EndFraction)? StartFraction StartRoot 15 EndRoot + 1 Over 1 minus StartRoot 15 EndRoot EndFraction StartFraction negative StartRoot 15 EndRoot + 1 Over 1 + StartRoot 15 EndRoot EndFraction StartFraction StartRoot 15 EndRoot + 1 Over 1 + StartRoot 15 EndRoot EndFraction StartFraction negative StartRoot 15 EndRoot minus 1 Over 1 minus StartRoot 15 EndRoot EndFraction

Answer 1

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

Answer 2

Answer:

$\tan(A - \frac{\pi}{4}) = \frac{-\sqrt{15}- 1}{1 -\sqrt{15}}$

Step-by-step explanation:

Given

$\tan A =-\sqrt{15$

Required

Find $\tan(A - \frac{\pi}{4})$

In trigonometry:

$\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$

This gives:

$\tan(A - \frac{\pi}{4}) = \frac{\tan A - \tan \frac{\pi}{4}}{1 + \tan A \tan \frac{\pi}{4}}$

$tan \frac{\pi}{4} = 1$

So:

$\tan(A - \frac{\pi}{4}) = \frac{\tan A - 1}{1 + \tan A * 1}$

$\tan(A - \frac{\pi}{4}) = \frac{\tan A - 1}{1 + \tan A}$

This gives:

$\tan(A - \frac{\pi}{4}) = \frac{-\sqrt{15}- 1}{1 -\sqrt{15}}$