Solve the following equations: + 2x+ 3=0 - Vidyadip

Question

Solve the following equations:
$\sin\text{x}+\sin2\text{x}+\sin3=0$

✓

Answer

We have,
$\sin\text{x}+\sin2\text{x}+\sin3=0$
$\Rightarrow\sin2\text{x}+2\sin2\text{x}.\cos\text{x}=0$
$\Rightarrow\sin2\text{x}+(1+2\cos\text{x})=0$
$\Rightarrow\text{Either}$
$\sin2\text{x}=0$ or $1+2\cos\text{x}=0$
$\Rightarrow2\text{x}=\text{n}\pi,\text{n}\in\text{z}$ or $\cos\text{x}=-\frac{1}{2}=\cos\Big(\pi-\frac{\pi}{3}\Big)$
$\Rightarrow\text{x}=\frac{\text{n}\pi}{2},\text{n}\in\text{z}$ or $\text{x}=2\text{m}\pi\pm\frac{2\pi}{3},\text{m}\in\text{z}$
Thus,
$\text{x}=\frac{\text{n}\pi}{2},\text{n}\in\text{z}$ or $\text{x}=2\text{m}\pi\pm\frac{2\pi}{3},\text{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.

Start Generating Free

Explore more

More "5 Marks Questions" from Trigonometric Equations→Trigonometric Equations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?

Prove that:
$\frac{\sin5\text{A}-\sin7\text{A}+\sin8\text{A}-\sin4\text{A}}{\cos4\text{A}+\cos7\text{A}-\cos5\text{A}-\cos8\text{A}}=\cot6\text{A}$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\frac{\text{x}^{\text{n}}-3^\text{n}}{\text{x}-\text{3}}=108,$ find the value of n.

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Show that the complex number z, satisfy the condition $\arg\Big(\frac{\text{z}-1}{\text{z}+1}\Big)=\frac{\pi}{4}$ lies on a circle.

The distributive law from algebra states that for all real numbers c, $a_1$ and $a_2,$ we have $c(a_1 + a_2)=ca_1 + ca_2.$
Use this law and mathematical induction to prove that, for all natural numbers $\text{n}\geq2,$ if c, $a_1, a_2, ...,$ an are any real numbers, then $c(a_1 + a_2 +...+ a_{n)}= ca_1 + ca_2 +...+ ca_n.$

If a, b, c are in A.P., prove that:
$\text{a}^3+\text{c}^3+6\text{abc}=8\text{b}^3$

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, mathematics, physics and chemistry are given below:

Subject	Mathematics	Physics	Chemistry
Mean	42	32	40.9
Standard	12	15	20
Deviation

Which of the three subjects shows the highest variability in marks and which shows the lowest?

Given $\text{a}_1=\frac{1}{2}\Big(\text{a}_0+\frac{\text{A}}{\text{a}_0}\Big),\text{a}_2=\frac{1}{2}\Big(\text{a}_1+\frac{\text{A}}{\text{a}_1}\Big)$ and $\text{a}_{\text{n}+1}=\frac{1}{2}\Big(\text{a}_\text{n}+\frac{\text{A}}{\text{a}_\text{n}}\Big)$ for $\text{n}\geq2,$ Where a > 0, A > 0. Prove that $\frac{\text{a}_{\text{n}}-\sqrt{\text{A}}}{{\text{a}_{\text{n}}+\sqrt{\text{A}}}}=\Bigg(\frac{\text{a}_{\text{1}}-\sqrt{\text{A}}}{\text{a}_{\text{1}}+\sqrt{\text{A}}}\Bigg)^{2^{\text{n}-1}}$

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:$\text{x}^2+4\text{y}^2-2\text{x}=0$