Find the general solution of : cosec =2 - Vidyadip

Question

Find the general solution of : $\operatorname{cosec} \theta=2$

✓

Answer

Solultion : (i) We have $\operatorname{cosec} \theta=2 \therefore \sin \theta=\frac{1}{2}$
$
\therefore \quad \sin \theta=\sin \frac{\pi}{6}
$
The general solution of $\sin \theta=\sin \alpha$ is $\theta=n \pi+(-1)^{ n } \alpha$, where $n \in Z$.
$\therefore \quad$ The general solution of $\sin \theta=\sin \frac{\pi}{6} \quad$ is $\theta=n \pi+(-1)^n \frac{\pi}{6}$, where $n \in Z$.
$\therefore \quad$ The general solution of $\operatorname{cosec} \theta=2$ is $\theta=n \pi+(-1)^n \frac{\pi}{6}$, where $n \in Z$.

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 "Solve the Following Question.(2 Marks)" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate the following integrals:$\int\frac{\text{e}^\text{x}}{1+\text{e}^{2\text{x}}}\text{dx}$

Write the value of $\hat{\text{i}}\times\big(\hat{\text{j}}+\hat{\text{k}}\big)+\hat{\text{j}}\times\big(\hat{\text{k}}+\hat{\text{i}}\big)+\hat{\text{k}}\times\big(\hat{\text{i}}+\hat{\text{j}}\big).$

A bag consists of $10$ balls each marked with one of the digits $0$ to $9.$ If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit $0?$

For each of the following p.d.f. of r.v. $X$, find (a) $P(X<1)$ and (b) $P(|X|<1)$ : $f(x)=\frac{x^2}{18}, \quad$ for $-3<x<3$ and $=0$, otherwise.

Passing through the origin and having slopes $2$ and $3$.

Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}\text{(x}-\text{a})\sin\Big(\frac{1}{\text{x}-\text{a}}\Big), & \text{x} \neq 0\\\ \ 0, & \text{x} = \text{a}\end{cases}\text{at x}=\text{a}$

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three mutually perpendicular unit vectors, then prove that $\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|=\sqrt{3}$

Evaluate the following integrals:$\int\limits^1_0 \frac{1}{1+\text{x}^2}\text{ dx}$

$\int \sqrt{1+\sin 5 x} \cdot d x$

Find the volume of the parallelopiped with its edges represented by the vectors
$\hat{\text{i}}+\hat{\text{j}},\hat{\text{i}}+2\hat{\text{j}}$ and $\hat{\text{i}}+\hat{\text{j}}+\pi{\text{k}}.$