Question
Solve the following equations:
$\tan\text{x}+\tan2\text{x}+\tan3\text{x}=0$
$\tan\text{x}+\tan2\text{x}+\tan3\text{x}=0$
✓
Answer
$\tan\text{x}+\tan2\text{x}+\frac{(\tan\text{x}+\tan2\text{x})}{1-\tan\text{x}.\tan2\text{x}}=0$
$[\tan\text{x}+\tan2\text{x}]\Big[1+\frac{1}{1-\tan\text{x}.\tan2\text{x}}\Big]=0$
$\tan\text{x}+\tan2\text{x}(2-\tan\text{x}.\tan2\text{x})=0$
$\tan\text{x}=\tan(-2\text{x})$ or $\tan\text{x}.\tan2\text{x}=0$
$\text{x}=\text{n}\pi-2\text{x}$ or $\tan\text{x}.\frac{2\tan\text{x}}{1-\tan^{2}\text{x}}=2$
$3\text{x}=\text{n}\pi$ or $\frac{2\tan^{2}\text{x}}{1-\tan^{2}\text{x}}=2$
$3\text{x}=\text{n}\pi$ or $2\tan^{2}\text{x}=2-2\tan^{2}\text{x}$
$3\text{x}=\text{n}\pi$ or $4\tan^{2}\text{x}=2$
$\text{x}=\frac{\text{n}\pi}{3}$ or $\tan^{2}\text{x}=\frac{1}{2}$
$\text{x}=\frac{\text{n}\pi}{3}$ or $\text{x}=\text{m}\pi\pm\tan^{-1}(\frac{1}{\sqrt{2}}),\text{n,m}\in\text{Z}$
$[\tan\text{x}+\tan2\text{x}]\Big[1+\frac{1}{1-\tan\text{x}.\tan2\text{x}}\Big]=0$
$\tan\text{x}+\tan2\text{x}(2-\tan\text{x}.\tan2\text{x})=0$
$\tan\text{x}=\tan(-2\text{x})$ or $\tan\text{x}.\tan2\text{x}=0$
$\text{x}=\text{n}\pi-2\text{x}$ or $\tan\text{x}.\frac{2\tan\text{x}}{1-\tan^{2}\text{x}}=2$
$3\text{x}=\text{n}\pi$ or $\frac{2\tan^{2}\text{x}}{1-\tan^{2}\text{x}}=2$
$3\text{x}=\text{n}\pi$ or $2\tan^{2}\text{x}=2-2\tan^{2}\text{x}$
$3\text{x}=\text{n}\pi$ or $4\tan^{2}\text{x}=2$
$\text{x}=\frac{\text{n}\pi}{3}$ or $\tan^{2}\text{x}=\frac{1}{2}$
$\text{x}=\frac{\text{n}\pi}{3}$ or $\text{x}=\text{m}\pi\pm\tan^{-1}(\frac{1}{\sqrt{2}}),\text{n,m}\in\text{Z}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.
One diameter of the circle circumscribing the rectangle ABCD is 4y = x + 7. If the coordinates of Aand B are (-3, 4) and (5, 4) respectively, find the equation of the circle.
The equation of the base of an equilateral triangle is x + y = 2 and its vertex is (2, -1). Find the length and equations of its sides.
Sketch the graphs of the following trigonometric functions:
$\text{h(x)}=\cos^22\text{x}$
→$\text{h(x)}=\cos^22\text{x}$
If in a $\triangle\text{ABC},\cos^2\text{A}+\cos^2\text{B}+\cos^2\text{C}=1,$ prove that the triangle is right angled.
→Find the equation of the hyperbola whose
→Foci at $(\pm2, 0)$ and eccentricity is $\frac{3}{2}$. [NCRT EXEMPLAR]
Find the number of words formed by permuting all the letters of the following words:
SERIES.
SERIES.
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections $($for instance, $\text{P}(\text{A}\cap\text{B})=.07)$ Determine:
→ - $\text{P(A)}$
- $\text{P}(\text{B}\cap\bar{\text{C}})$
- $\text{P(A}\cup\text{B})$
- $\text{P(A}\cap\bar{\text{B}})$
- $\text{P(B}\cap\text{C})$
- Probability of exactly one of the three occurs.
If A(-2, 2, 3) and B(13, -3, 13) are two points. Find the locus of a point P which moves in such a way that 3PA = 2PB.
If $\text{a},\ \text{b},\ \text{c}$ are in A.P., then show that:
$\text{bc}-\text{a}^2,\ \text{ca}-\text{b}^2,\ \text{ab}-\text{c}^2$ are in A.P.
→$\text{bc}-\text{a}^2,\ \text{ca}-\text{b}^2,\ \text{ab}-\text{c}^2$ are in A.P.