CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Introduction to Angle

If tan a, tan...

Question

If $tan a, tan b$ are the roots of $x^{2} - p x + q = 0$ and $cot a, cot b$ are the roots of $x^{2} - r x + s = 0$ , then the value of $r s$ is

Open in App

Solution

$x^{2} - p x + q = 0$
$tan a + tan b = p, tan a tan b = q$
$x^{2} - r x + s = 0$
$cot a + cot b = r, cot a cot b = s$

Now,
$r s = (cot a + cot b) cot a cot b$
$= (\frac{1}{tan a} + \frac{1}{tan b}) \frac{1}{tan a tan b}$
$= \frac{tan a + tan b}{(tan a tan b)^{2}} = \frac{p}{q^{2}}$

Suggest Corrections

thumbs-up

0

Similar questions

tan a, tan b

are the roots of

x^{2} - p x + q = 0

cot a, cot b

are the roots of

x^{2} - r x + s = 0

, then the value of

r s

If $tan A$ and $tan B$ are the roots of the equation $x^{2} - p x + q = 0$ , then the value of ${sin}^{2} (A + B)$ is

tan A

tan B

are the roots of the quadratic equation

x^{2} - p x + q = 0

{sin}^{2} (A + B) =

Q. A, B, C are the angles of a triangle such that

tan A, tan B, tan C

are three roots of the biquadratic

x^{4} - p x^{3} + q x^{2} - r x + s = 0

. Prove that the fourth root satisfies

x^{2} - p x + s = 0

If $α, β$ be the roots of $x^{2} + p x + q = 0$ and $α + h, β + h$ are the roots of $x^{2} + r x + s = 0$ , then

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Introduction to Angle

Standard XIII Mathematics

Join BYJU'S Learning Program

CrossIcon