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

StartFraction StartRoot 15 EndRoot + 1 Over 1 minus StartRoot 15 EndRoot EndFraction

Explanation:

EndRoot EndFraction StartFraction negative StartRoot 15 EndRoot + 1 Over 1 + StartRoot 15 EndRoot EndFraction

Answer 2

`\tan(A - (\pi)/(4)) = (-√(15)- 1)/(1 -√(15))`

Explanation:

Given

`\tan A =-\sqrt{15`

Required

Find
`\tan(A - (\pi)/(4))`

In trigonometry:

`\tan(A - B) = (\tan A - \tan B)/(1 + \tan A \tan B)`

This gives:

`\tan(A - (\pi)/(4)) = (\tan A - \tan (\pi)/(4))/(1 + \tan A \tan (\pi)/(4))`

`tan (\pi)/(4) = 1`

So:

`\tan(A - (\pi)/(4)) = (\tan A - 1)/(1 + \tan A * 1)`

`\tan(A - (\pi)/(4)) = (\tan A - 1)/(1 + \tan A)`

This gives:

`\tan(A - (\pi)/(4)) = (-√(15)- 1)/(1 -√(15))`