Find the value of tan 8 . - Vidyadip

Question

Find the value of tan $\frac { \pi } { 8 }$.

✓

Answer

Suppose, $x =$ $\frac { \pi } { 8 }$
Then, $2x =$ $\frac { \pi } { 4 }$
Now, $ tan 2x =$ tan $\frac { \pi } { 4 }$
$\Rightarrow \quad \frac { 2 \tan x } { 1 - \tan ^ { 2 } x } = \tan \frac { \pi } { 4 }$ [$\because$$ tan 2x =$ $\frac { 2 \tan x } { 1 - \tan ^ { 2 } x }$]
Putting x = $\frac { \pi } { 8 }$,
$\Rightarrow \frac { 2 \tan \frac { \pi } { 8 } } { 1 - \tan ^ { 2 } \frac { \pi } { 8 } }$$ = 1$
Let y = tan $\frac { \pi } { 8 }$
Then, $\frac { 2 y } { 1 - y ^ { 2 } }$ = 1
$\Rightarrow$ $2y = 1 - y^2$
$\Rightarrow$ $y^2 + 2y - 1 = 0$
$\therefore$ y = $\frac { - 2 \pm \sqrt { ( 2 ) ^ { 2 } + 4 } } { 2 } = \frac { - 2 \pm \sqrt { 8 } } { 2 } = \frac { - 2 \pm 2 \sqrt { 2 } } { 2 }$
$\Rightarrow$ y = - 1 $\pm \sqrt { 2 }$
But $\frac { \pi } { 8 }$ lies in I quadrant, so y = tan $\frac { \pi } { 8 }$ is positive.
Hence, tan $\frac { \pi } { 8 }$ = - 1 + $\sqrt { 2 }$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Trigonometric Functions→Trigonometric Functions — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
4x² + 9y² = 36

Solve the following linear inequations in R:
$\frac{2\text{x}-3}{3\text{x}-7}>0$

$\text{b}(\text{c}\cos\text{A}-\text{a}\cos\text{C})=\text{c}^2-\text{a}^2$

How many terms of the A.P. $-6,\ -\frac{11}{2},\ 5,\ ...$ are needed to give the sum -25?

Find all pairs of consecutive odd positive integers, both of which are smaller than 10, such that their sum is more than 11.

In a survey of 100 persons it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A and B, 10 read magazines A and C, 5 read magazines B and C and 3 read all the three magazines?

How many read none of three magazines?
How many read magazine C only?

Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
$\frac{{{x^2}}}{4} + \frac{{{y^2}}}{{25}} = 1$

To receive Grade 'A', in a course, one must obtain an average of 90 marks or more in five examinations (each of 100 marks). If Sunita's marks in first four examinations are 87, 92, 94. and 95, find minimum marks that Sunita must obtain in fifth examination to get Grade 'A' in the course.

If $e$ and $e^{\prime}$ be the eccentricity of a hyperbola and its conjugate, then prove that $\frac{1}{e^2}+\frac{1}{\left(e^{\prime}\right)^2}=1$.

Find the mean deviation about the mean of the distribution:

Size	20	21	22	23	24
Frequency	6	4	5	1	4