If A + B + C = π, prove that
$\sin 2 A+\sin 2 B-\sin 2 C=4 \cos A \cos B \sin C$
$=\sin 2 A+\sin 2 B-\sin 2 C$
$=2 \sin (B+C) \cos A+2 \sin (A+C) \cos B-2 \sin (A+B) \cos C$
Using formula, $\sin (A+B)=\sin A \cos B+\cos A \sin B$
$=\sin 2 \mathrm{~A}+\sin 2 \mathrm{~B}-\sin 2 \mathrm{C}$
Using formula
sin2A = 2sinAcosA
= 2sinAcosA + 2sinBcosB - 2sinCcosC
Since A + B + C = π
$\rightarrow \mathrm{B}+\mathrm{C}=180-\mathrm{A}$
And $\sin (\pi-A)=\sin A$
$=2 \sin (B+C) \cos A+2 \sin (A+C) \cos B-2 \sin (A+B) \cos C$
$=2(\sin B \cos C+\cos B \sin C) \cos A+2(\sin A \cos C+\cos A \sin C) \cos B-2(\sin A \cos B+$
$\cos A \sin B) \cos C$
$=2 \cos A \sin B \cos C+2 \cos A \cos B \sin C+2 \sin A \cos B \cos C+2 \cos A \cos B \sin C-$
$2 \sin A \cos B \cos C-2 \cos A \sin B \cos C$
$=2 \cos A \cos B \sin C+2 \cos A \cos B \sin C$
$=4 \cos A \cos B \sin C$
= R.H.S
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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,