Find the general solution of each of the following equations:
4sin x cos x + 2sin x + 2cos x + 1 = 0
To Find: General solution.
Given: $4 \sin x \cos x+2 \sin x+2 \cos x+1=0 \Rightarrow 2 \sin x(2 \cos x+1)+2 \cos x+1=0$
So $(2 \cos x+1)(2 \sin x+1)=0$
$\cos x=\frac{-1}{2}=\cos \left(\frac{2 \pi}{3}\right)$ or $\sin x=\frac{-1}{2}=\sin \frac{7 \pi}{6}$
Formula used: $\cos \theta=\cos \alpha \Rightarrow \theta=2 \mathrm{n} \pi \pm \alpha$ or $\sin \theta=\sin \alpha \Rightarrow \theta=\mathrm{m} \pi+(-1)^{\mathrm{m}} \alpha$ where $n, m \in I$
$x=2 n \pi \pm \frac{2 \pi}{3}$ or $x=m \pi+(-1)^{m} \cdot \frac{7 \pi}{6}$ where $n, m \in \mid$
So the general solution is $x=2 n \pi \pm \frac{2 \pi}{3}$ or $x=m \pi+(-1)^{m} \cdot \frac{7 \pi}{6}$ where $n, m \in I$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,