Find the principal and general solution of the equation: cosec x … - Vidyadip

Question

Find the principal and general solution of the equation: cosec x = -2

✓

Answer

Here cosec x = - 2 $ \Rightarrow \sin x = - \frac{1}{2}$, which is negative, so x lies in third or fourth quadrant.
$\therefore \sin x=-\frac{1}{2}=-\sin 30^{\circ}=\sin \left(180^{\circ}+30^{\circ}\right) \text { or } \sin \left(360^{\circ}-30^{\circ}\right)$
$ =\sin 210^{\circ} \text { or } \sin 330^{\circ}$
$ = \sin \frac{{7\pi }}{6}$ or $\sin \frac{{11\pi }}{6}$
Hence the principal solutions are $\frac{{7\pi }}{6},\frac{{11\pi }}{6}$
Now $\sin x = - \sin \frac{\pi }{6}$
$ \Rightarrow x = n\pi + {( - 1)^n}\left( {\frac{{7\pi }}{6}} \right)$ 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 "(Each question 1 marks)" from TRIGONOMETRIC FUNCTIONS→TRIGONOMETRIC FUNCTIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Is the collection of most dangerous animals of the world set? Justify your answer.

Find the derivative of $2x - \frac{3}{4}$

Write the negation of the following statements: s: There exists a number x such that 0 < x < 1.

Evaluate the following limits in Exercise: $\lim\limits_{\text{x} \rightarrow4}\frac{4\text{x}+3}{\text{x}-2}$

If ${^\text{35}}\text{C}_{\text{n}+7}={^\text{35}}\text{C}_{\text{4n-2}},$ then write the values of n.

Show that the statement: p : "If x is a real number such that $x ^3+ x =0$, then x is $0^{\text {" }}$ is true by. Method of contradition.

State whether the “Or” used in the following statements is “exclusive “or” inclusive. Give reasons for your answer. To apply for a driving licence, you should have a ration card or a passport.

Which of the following can not be valid assignment of probabilities for outcomes of sample Space S = $\{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$

Assignment	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$\omega_{4}$	$\omega_{5}$	$\omega_{6}$	$\omega_{7}$
	-0.1	0.2	0.3	0.4	-0.2	0.1	0.3

If S and T are two sets such that S has 21 elements T has 32 elements and$S \cap T$has 11 elements, how many elements does$S \cup T$have?

On her vacations Veena visits four cities (A, B, C and D) in a random order. What is the probability of A either first or second?