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# PRECIZE Algebra & Trigonometry

355.00

The present book is strictly in accordance with the latest syllabus implemented by Panjab University, Chandigarh as per NEP 2020. It is the culmination of honest and sincere efforts on the part of the authors to meet the requirements of students who opt for mathematics at the Graduation level. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner to meet the various needs of all types of learners. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems so that the study leads to perfect clarity and understanding. A large number of notes and remarks have been added for a better understanding of the subject. Well-planned exercises have been given in each chapter to provide the students with an opportunity of exhaustive practice. At the end of the each chapter, REVIEW OF THE CHAPTER has been introduced so that the students can revise the chapter at a glance.

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## Description

Principle of Mathematical Induction, Recall of Binomial Theorem for positive index, General and Middle terms in Binomial expansions, Properties of Binomial coefficients, Binomial Theorem for any index, Summation of infinite Binomial series.

Solution of Trigonometric Equations, Sine, Cosine and Projection formulae for triangles, De Moivre’s theorem, applications of De Moivre’s theorem including primitive nth root of unity. Expansions of sin nθ , cos nθ , , (n∈N). The exponential, logarithmic, direct and inverse circular and hyperbolic functions of a complex variable.

Recall of determinant of a matrix, Properties of determinants, Hermitian and skew-Hermitian matrices, linear dependence of row and column vectors, row rank, column rank and rank of a matrix and their equivalence.

Theorems on consistency of a system of linear equations (both homogeneous and non-homogeneous). Eigen-values, eigen-vectors and characteristic equation of a matrix, Cayley-Hamilton theorem and its use in finding inverse of a matrix. Diagonalization.