Question:
Find the general solution of each of the following equations:
cot x + tan x = 2 cosec x
Solution:
To Find: General solution.
Given: $\cot x+\tan x=2 \operatorname{cosec} x \Rightarrow \cos ^{2} x+\sin ^{2} x=2 \sin x \cos x \operatorname{cosec} x \Rightarrow 1=\sin 2 x$ cosec $x$
$\Rightarrow \operatorname{cosec} 2 x=\operatorname{cosec} x \Rightarrow \sin x=\sin 2 x \Rightarrow \sin x=2 \sin x \cos x \Rightarrow \sin x=0$ or $\cos$
$x=\frac{1}{2}=\cos (1)$
Formula used: $\sin \theta=0 \Rightarrow \theta=n \pi, \cos \theta=\cos \alpha \Rightarrow \theta=2 n$
By using above formula, we have
$x=n \pi$ or $x=2 m \pi \pm \frac{\pi}{3}$ where $n, m$ I
So general solution is $x=n \pi$ or $x=2 m \pi \pm \frac{\pi}{3}$ where $n, m \in$ ।
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- 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,
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