In any ΔABC, prove that
$\left(c^{2}-a^{2}+b^{2}\right) \tan A=\left(a^{2}-b^{2}+c^{2}\right) \tan B=\left(b^{2}-c^{2}+a^{2}\right) \tan C$
Need to prove: $\left(c^{2}-a^{2}+b^{2}\right) \tan A=\left(a^{2}-b^{2}+c^{2}\right) \tan B=\left(b^{2}-c^{2}+a^{2}\right) \tan C$
We know
$\tan A=\frac{a b c}{R} \frac{1}{b^{2}+c^{2}-a^{2}}-\cdots-\cdots(a)$
Similarly, $\tan B=\frac{a b c}{R} \frac{1}{c^{2}+a^{2}-b^{2}}$ and $\tan C=\frac{a b c}{R} \frac{1}{a^{2}+b^{2}-c^{2}}$
Therefore,
$\left(b^{2}+c^{2}-a^{2}\right) \tan A=\frac{a b c}{R}[$ from $(a)]$
Similarly,
$\left(c^{2}+a^{2}-b^{2}\right) \tan B=\frac{a b c}{R}$ and $\left(a^{2}+b^{2}-c^{2}\right) \tan C=\frac{a b c}{R}$
Hence we can conclude comparing above equations,
$\left(c^{2}-a^{2}+b^{2}\right) \tan A=\left(a^{2}-b^{2}+c^{2}\right) \tan B=\left(b^{2}-c^{2}+a^{2}\right) \tan C$
[Proved]
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- Kinematics 1D
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- 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
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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,