AIEEE 2004 | Trigonometric Ratio and Identites Question 51 | Mathematics

Let $$\alpha ,\,\beta $$ be such that $$\pi < \alpha - \beta < 3\pi $$.
If $$sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}$$ and $$\cos \alpha + \cos \beta = - {{27} \over {65}}$$ then the value of $$\cos {{\alpha - \beta } \over 2}$$ :

$${{ - 6} \over {65}}\,\,$$

$${3 \over {\sqrt {130} }}$$

$${6 \over {65}}$$

$$ - {3 \over {\sqrt {130} }}$$

Questions Asked from Trigonometric Ratio and Identites (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

JEE Main Subjects

Physics

Mechanics

Units & Measurements Vector Algebra Motion Circular Motion Laws of Motion Work Power & Energy Center of Mass and Collision Rotational Motion Properties of Matter Heat and Thermodynamics Simple Harmonic Motion Waves Gravitation

Electricity

Electrostatics Current Electricity Capacitor Magnetic Effect of Current Magnetic Properties of Matter Electromagnetic Induction Alternating Current Electromagnetic Waves

Optics

Geometrical Optics Wave Optics

Modern Physics

Atoms and Nuclei Dual Nature of Radiation Semiconductor Communication Systems

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Structure of Atom Redox Reactions Gaseous State Chemical Equilibrium Ionic Equilibrium Solutions Thermodynamics Electrochemistry Chemical Kinetics and Nuclear Chemistry Solid State Surface Chemistry

Inorganic Chemistry

Periodic Table & Periodicity Chemical Bonding & Molecular Structure Isolation of Elements Hydrogen s-Block Elements p-Block Elements d and f Block Elements Coordination Compounds Environmental Chemistry

Organic Chemistry

Basics of Organic Chemistry Hydrocarbons Haloalkanes and Haloarenes Alcohols, Phenols and Ethers Aldehydes, Ketones and Carboxylic Acids Compounds Containing Nitrogen Polymers Biomolecules Chemistry in Everyday Life Practical Organic Chemistry

Mathematics

Algebra

Sets and Relations Logarithm Quadratic Equation and Inequalities Sequences and Series Mathematical Induction Binomial Theorem Matrices and Determinants Permutations and Combinations Probability Vector Algebra 3D Geometry Complex Numbers Statistics Mathematical Reasoning

Trigonometry

Trigonometric Ratio and Identites Trigonometric Equations Inverse Trigonometric Functions Properties of Triangle Height and Distance

Coordinate Geometry

Straight Lines and Pair of Straight Lines Circle Parabola Ellipse Hyperbola

Calculus

Functions Limits, Continuity and Differentiability Differentiation Application of Derivatives Indefinite Integrals Definite Integration Area Under The Curves Differential Equations