Download App

Trigonometric Equations — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSTrigonometric Equations5 Marks
Question
Solve the following equations:
$\sin\text{x}\ \tan\text{x}-1\tan\text{x}-\sin\text{x}$
✓

Answer

$\sin\text{x}\ \tan\text{x}-1=\tan\text{x}-\sin\text{x}$
$=\sin\text{x}\ \text{tan}\text{x}-\tan\text{x}+\sin\text{x}-1=0$
$\Rightarrow\tan\text{x}(\sin\text{x}-1)+1(\sin\text{x})-1=0$
$\Rightarrow(\tan\text{x}+1)(\sin\text{x}-1)=0$
$\Rightarrow(\tan\text{x}+1)=0$ or $(\sin\text{x}-1)=0$
$\Rightarrow\tan\text{x}=-1$ or $\sin\text{x}=1$
$\Rightarrow\tan\text{x}=\tan\frac{3\pi}{4}$ or $\sin\text{x}=\sin\frac{\pi}{2}$
$\Rightarrow\text{x}=\text{n}\pi+\frac{3\pi}{4}$ or $\text{x}=\text{n}\pi+(-1)^\text{n}\frac{\pi}{2},\ \text{n}\in\text{Z}$

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→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Find the coefficient of variation for the following data:
Size (in cms):
10-15
15-20
20-25
 25-30 30-35 35-40
No. of items:
 2
 
8
20
 35 20 15
→
Differentiate the following from the first principle

$\text{f}(\text{x})=\frac{\sin\text{x}}{\text{x}}$

→
In each of the followin find the equation of the hyperbola satisying the given conditions:
vertices $(0, \pm5), $ foci $(0,\pm8)$ [NCERT]
→
In a potato race 20 potatoes are placed in a line at intervals of 4 meters with the first potato 24 metres from the starting point. A contestant is required to bring the potatoes back to the starting place one at a time. How far would he run in bringing back all the potatoes?
→
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
→
Differentiate the following from first principle:

$\frac{\text{x}+1}{\text{x}+2}$

→
Prove that
$\cos\frac{\pi}{65}\cos\frac{2\pi}{65}\cos\frac{4\pi}{65}\cos\frac{8\pi}{65}\cos\frac{16\pi}{65}\cos\frac{32\pi}{65}=\frac{1}{64}$
→
Solve the following system of equations in R.
$\frac{1}{|\text{x}|-3}<\frac{1}{2}$
→
Find the equation of the circle whose diameter is the line segment joining (-4, 3) and (12, -1). Find also the intercept made by it on y-axis.
→
Match the questions given under Column I with their appropriate answers given under the Column II.
Column I Column II
(a) $1^2+2^2+3^2+....+\text{n}^2$ (i) $\Big[\frac{\text{n}(\text{n}+1)}{2}\Big]^2$
(b) $1^3+2^3+3^3+....\text{n}^3$ (ii) $\text{n}(\text{n}+1)$
(c) $2+4+6+....+2\text{n}$ (iii) $\frac{\text{n}(\text{n}+1)(2\text{n}+1)}{6}$
(d) $1+2+3+....\text{n}$ (iv) $\frac{\text{n}(\text{n}+1)}{2}$
→