Question:
If $\tan \theta=\frac{a}{b}$, find the value of $\frac{\cos \theta+\sin \theta}{\cos \theta-\sin \theta}$.
Solution:
Given:
$\tan \theta=\frac{a}{b} \ldots \ldots$(1)
Now, we know that $\tan \theta=\frac{\sin \theta}{\cos \theta}$
Therefore equation (1) becomes as follows
$\frac{\sin \theta}{\cos \theta}=\frac{a}{b}$
Now, by applying invertendo
We get,
$\frac{\cos \theta}{\sin \theta}=\frac{b}{a}$
Now, by applying Compenendo-dividendo
We get,
$\frac{\cos \theta+\sin \theta}{\cos \theta-\sin \theta}=\frac{b+a}{b-a}$
Therefore,
$\frac{\cos \theta+\sin \theta}{\cos \theta-\sin \theta}=\frac{b+a}{b-a}$
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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,
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