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- Khuram Ali Khan
- <[email protected]>\\ \\ **Field of Research:** Difference and functional equations, Real functions, Mathema... - Khuram Ali Khan, Josip Pečarić and Ivan Perić, Differences of Weighted Mixed Symmetric Means and Related Re... Behavior of a competitive system of second-order difference equations, The Scientific World Journal, Vol. 201... en, Stability Analysis of a System of Exponential Difference Equations, Discrete Dynamics in Nature and Societ
- FSc Part 1 (KPK Boards) @fsc
- ries and its sum of $n$ terms. * know method of differences and its uses. * use the partial fraction to fi... = Chapter 10: Trigonometric Identities of Sum and Difference of Angles ===== === Objectives === After reading ... xpress the product of sines and cosines as sum or differences of sines and cosines. * express the sums or differences of sines and cosines as product. ===Download=== <
- Atiq ur Rehman, PhD
- rg>, <[email protected]> **Field of Research:** Difference and functional equations, Real functions, Inequal... Y. Mehboob, Mean value theorems associated to the differences of Opial–type inequalities and their fractional ... convex functions and related results, Advances in Difference Equations, 2020:163, (2020), 1-18. 46. L. N. Mis... iated results in fractional calculus, Advanced in Difference Equations, 2019:152 (2019), 1-13. 44. G. Farid,
- Numerical Analysis II @notes
- | ====Summary & contents==== * Operator * Difference Equation * Homogeneous Linear Difference Equation * Non-Homogeneous Linear Difference Equation * Non-Homogeneous Difference Equation * Formation of Difference Equation * Numerical Integrati
- Question 1, Exercise 10.3 @fsc-part1-kpk:sol:unit10
- 3 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat... =Question 1(i)===== Express the product as sum or difference $2\sin 6x\sin x$. ====Solution==== We have an id... Question 1(ii)===== Express the product as sum or difference $\sin {{55}^{\circ }}\cos {{123}^{\circ }}$. ====... uestion 1(iii)===== Express the product as sum or difference: $$\sin \dfrac{A+B}{2}\cos \dfrac{A-B}{2}.$$ ====
- Question 2, Exercise 10.3 @fsc-part1-kpk:sol:unit10
- 3 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat... istan. =====Question 2(i)===== Convert the sum or difference as product: $$\sin {{37}^{\circ }}+\sin {{43}^{\c... $$ =====Question 2(ii)===== Convert the sum or difference as product $\cos {{36}^{\circ }}-\cos {{82}^{\cir... .$$ =====Question 2(iii)===== Convert the sum or difference as product: $$\sin \dfrac{P+Q}{2}-\sin \dfrac{P-Q
- Question 1, Exercise 10.3 @math-11-kpk:sol:unit10
- 3 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat... =Question 1(i)===== Express the product as sum or difference $2\sin 6x\sin x$. ====Solution==== We have an id... Question 1(ii)===== Express the product as sum or difference $\sin {{55}^{\circ }}\cos {{123}^{\circ }}$. ====... uestion 1(iii)===== Express the product as sum or difference: $$\sin \dfrac{A+B}{2}\cos \dfrac{A-B}{2}.$$ ====
- Question 2, Exercise 10.3 @math-11-kpk:sol:unit10
- 3 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat... istan. =====Question 2(i)===== Convert the sum or difference as product: $$\sin {{37}^{\circ }}+\sin {{43}^{\c... $$ =====Question 2(ii)===== Convert the sum or difference as product $\cos {{36}^{\circ }}-\cos {{82}^{\cir... .$$ =====Question 2(iii)===== Convert the sum or difference as product: $$\sin \dfrac{P+Q}{2}-\sin \dfrac{P-Q
- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) @fsc-part1-kpk:sol
- ==== Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) ===== This is a tenth unit... ess the product (of sines and cosines) as sums or differences (of sines and cosines) * Express the sums or differences (of sines and cosines) as products (of sines and
- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) @math-11-kpk:sol
- ==== Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) ===== This is a tenth unit... ess the product (of sines and cosines) as sums or differences (of sines and cosines) * Express the sums or differences (of sines and cosines) as products (of sines and
- Unit 05: Miscellaneous Series (Solutions) @math-11-kpk:sol
- rithmetico-geometric series. * Define method of differences. * Use this method to find the sum of $n$ terms of the series whose differences of the consecutive terms are either in arithmeti
- Question 1 Exercise 4.3 @math-11-kpk:sol:unit04
- ion==== Let $a_1$ be first term and $d$ be common difference of given A.P. Then \begin{align}&a_1=9 \\ &d=7-9... ion==== Let $a_1$ be first term and $d$ be common difference of given A.P. Then \begin{align}&a_1=3 \\ &d=\df
- Question 10 Exercise 4.4 @math-11-kpk:sol:unit04
- n. =====Question 10===== Find two numbers if the difference between them is $48$ and their A.M exceeds their ... two numbers be $a$ and $b$ \\ Condition-$1$\\ The difference between them is $48$\\ Therefore, $$\quad a-b=48.
- Question 9 Review Exercise @math-11-kpk:sol:unit05
- 13+21+31+\ldots$ ====Solution==== Using method of differences to compute the sum of the given series. \begin{a... +5+14+41+\ldots$ ====Solution==== Using method of differences to compute the sum of the given series. \begin{a
- MTH321: Real Analysis I (Spring 2023) @atiq
- n decimal notation, and insisted that there is no difference between rational and irrational numbers in this r