Download App

Trigonometric Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsTrigonometric Functions1 Mark
Question
State True or False for the following statement:
If $\tan\theta+\tan2\theta+\sqrt{3}\tan\theta\tan2\theta=\sqrt{3},$ then $\theta=\frac{\text{n}\pi}{3}+\frac{\pi}{9}$
✓

Answer

True.
Solution:
Given that, $\tan\theta+\tan2\theta=-\sqrt3\tan\theta\tan2\theta+\sqrt3$
$\Rightarrow\tan\theta+\tan2\theta=\sqrt3-\sqrt3\tan\theta\tan2\theta$
$\Rightarrow\tan\theta+\tan2\theta=\sqrt3(1-\tan\theta\tan2\theta)$
$\Rightarrow\frac{\tan\theta+\tan2\theta}{1-\tan\theta\tan2\theta}=\sqrt3$
$\Rightarrow\tan(\theta+2\theta)=\sqrt3$
$\Rightarrow\tan3\theta=\tan\frac{\pi}{3}\therefore3\theta=\text{n}\pi+\frac{\pi}{3}$
so $\theta=\frac{\text{n}\pi}{3}+\frac{\pi}{9}$
Hence, the given statement is 'true'.

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 "True False[1 Marks ]" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If |x| > 5, then $\text{x}\in(-\infty, -5)\cup(5, \infty).$
→
State True or False for the following statement:
$\sin10^\circ$ is greater than $\cos10^\circ.$
→
State which of the statement in True or False.
If the expansion of $\Big(\text{x}-\frac{1}{\text{x}^2}\Big)^{2\text{n}}$ contains a term independent of x, then n is a multiple of 2.
→
Given that M = {1, 2, 3, 4, 5, 6, 7, 8, 9} and if B = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then $\text{B} \not\subset \text{M}.$
→
If xy < 0, then x < 0 and y < 0.
→
State whether the following statements are true or false:
a $\subset$ {b, c, a}
→
State which of the following statements is True or False.
Graph of $\text{y}\geq0$ is:
→
Line joining the points (3, -4) and (-2, 6) is perpendicular to the line joining the points (-3, 6) and (9, -18).
→
Write the following statement are true? Justify your answer.
The sets P = {a} and B = {{a}} are equal.
→
State whether the statements are True or False.
The sum of probabilities of two students getting distinction in their final examinations is 1.2
→