
The general value of \[\theta \] satisfying \[sin2\theta + sin\theta = 2\]
A. \[n\pi + ( - 1)n\pi /6\]
B. \[2n\pi + \pi /4\]
C. \[n\pi + ( - 1)n\pi /2\]
D. \[n\pi + ( - 1)n\pi /3\]
Answer
161.1k+ views
Hint:
The most common value of is \[{\bf{\theta }} = {\bf{n}}{\rm{ }}{\bf{\pi }} + {\bf{\alpha }}\;\], obeying the equations \[sin{\rm{ }}\theta {\rm{ }} = {\rm{ }}sin{\rm{ }}\alpha \]and \[cos{\rm{ }}\theta {\rm{ }} = {\rm{ }}cos{\rm{ }}\alpha \].Finding all possible sets of values for that satisfy the given equation is the goal when attempting to solve a trigonometric problem. When an equation's graph can be easily drawn and the equation is simple,
Complete step by step solution: \[sin2\theta + sin\theta = 2\]
⟹\[sin\theta = 2 - 1 \pm 9 = - 2,{\bf{1}}\]
⟹\[sin\theta = - 2\;or\;sin\theta = 1\]
⟹\[\theta = n\pi + ( - 1)n2\pi \]
To stay competitive in the exams, students are urged to understand all of the trigonometric formulas, including the trigonometry fundamentals. To become familiar with the subject, students should practice a variety of trigonometry problems based on trigonometric ratios and the fundamentals of trigonometry.
If \[tan{\rm{ }}\theta \] or \[sec{\rm{ }}\theta \] is involved in the equation, \[\theta {\rm{ }} \ne \]odd multiple of \[\pi /2\].
If \[cot{\rm{ }}\theta \] or \[cosec{\rm{ }}\theta \] is involved in the equation, \[\theta {\rm{ }} \ne \]multiple of \[\pi \] or\[0\].
The y-value of point P on the unit circle represents the sine of the angle. Therefore, we indicate the two equal intervals in the graph since \[sin\theta {\rm{ }} = {\rm{ }}sin{\rm{ }}\left( {180 - \theta {\rm{ }}} \right).\]As a result, the graph is approximately \[90^\circ \] symmetric between \[0^\circ \]and \[180^\circ \]. Similarly, the graph is symmetric around \[270^\circ \]between \[180^\circ \] and \[360^\circ .\] A circle with a radius of one is referred to as a unit circle. The unit circle is frequently the circle with radius \[1\] that is centered at the origin, especially in trigonometry \[\left( {0,{\rm{ }}0} \right)\].
Option ‘C’ is correct
Note: There isn't a single way to solve trigonometric equations that can be defined. In each situation, the ability to solve a trigonometric equation successfully depends in part on the understanding and practical application of the trigonometric formula as well as problem-solving experience. For many trigonometric formulas, all of the values of the variables that appear in them are true equivalences.
The most common value of is \[{\bf{\theta }} = {\bf{n}}{\rm{ }}{\bf{\pi }} + {\bf{\alpha }}\;\], obeying the equations \[sin{\rm{ }}\theta {\rm{ }} = {\rm{ }}sin{\rm{ }}\alpha \]and \[cos{\rm{ }}\theta {\rm{ }} = {\rm{ }}cos{\rm{ }}\alpha \].Finding all possible sets of values for that satisfy the given equation is the goal when attempting to solve a trigonometric problem. When an equation's graph can be easily drawn and the equation is simple,
Complete step by step solution: \[sin2\theta + sin\theta = 2\]
⟹\[sin\theta = 2 - 1 \pm 9 = - 2,{\bf{1}}\]
⟹\[sin\theta = - 2\;or\;sin\theta = 1\]
⟹\[\theta = n\pi + ( - 1)n2\pi \]
To stay competitive in the exams, students are urged to understand all of the trigonometric formulas, including the trigonometry fundamentals. To become familiar with the subject, students should practice a variety of trigonometry problems based on trigonometric ratios and the fundamentals of trigonometry.
If \[tan{\rm{ }}\theta \] or \[sec{\rm{ }}\theta \] is involved in the equation, \[\theta {\rm{ }} \ne \]odd multiple of \[\pi /2\].
If \[cot{\rm{ }}\theta \] or \[cosec{\rm{ }}\theta \] is involved in the equation, \[\theta {\rm{ }} \ne \]multiple of \[\pi \] or\[0\].
The y-value of point P on the unit circle represents the sine of the angle. Therefore, we indicate the two equal intervals in the graph since \[sin\theta {\rm{ }} = {\rm{ }}sin{\rm{ }}\left( {180 - \theta {\rm{ }}} \right).\]As a result, the graph is approximately \[90^\circ \] symmetric between \[0^\circ \]and \[180^\circ \]. Similarly, the graph is symmetric around \[270^\circ \]between \[180^\circ \] and \[360^\circ .\] A circle with a radius of one is referred to as a unit circle. The unit circle is frequently the circle with radius \[1\] that is centered at the origin, especially in trigonometry \[\left( {0,{\rm{ }}0} \right)\].
Option ‘C’ is correct
Note: There isn't a single way to solve trigonometric equations that can be defined. In each situation, the ability to solve a trigonometric equation successfully depends in part on the understanding and practical application of the trigonometric formula as well as problem-solving experience. For many trigonometric formulas, all of the values of the variables that appear in them are true equivalences.
Recently Updated Pages
If there are 25 railway stations on a railway line class 11 maths JEE_Main

Minimum area of the circle which touches the parabolas class 11 maths JEE_Main

Which of the following is the empty set A x x is a class 11 maths JEE_Main

The number of ways of selecting two squares on chessboard class 11 maths JEE_Main

Find the points common to the hyperbola 25x2 9y2 2-class-11-maths-JEE_Main

A box contains 6 balls which may be all of different class 11 maths JEE_Main

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Displacement-Time Graph and Velocity-Time Graph for JEE

Degree of Dissociation and Its Formula With Solved Example for JEE

Free Radical Substitution Mechanism of Alkanes for JEE Main 2025

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

NCERT Solutions for Class 11 Maths Chapter 4 Complex Numbers and Quadratic Equations

NCERT Solutions for Class 11 Maths In Hindi Chapter 1 Sets

NCERT Solutions for Class 11 Maths Chapter 6 Permutations and Combinations
