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- Khuram Ali Khan
- <[email protected]>\\ \\ **Field of Research:** Difference and functional equations, Real functions, Mathema... 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... qualities for quasi-convex functions, Advances in Difference Equations ( Published January 18, 2019) IF 1.51 (
- 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
- Chapter 10: Trigonometric Identities of Sum and Difference of Angles @fsc:kpk_fsc_part_1
- = Chapter 10: Trigonometric Identities of Sum and Difference of Angles ====== Notes of Chapter 10: Trigonometric Identities of Sum and Difference of Angles of "A Textbook of Mathematics for Class... c_part_1:ch10-trigonometric-identities-of-sum-and-difference-of-angles-fsc1-kpk.pdf}} **{{:fsc:kpk_fsc_part_1:ch10-trigonometric-identities-of-sum-and-difference-of-angles-fsc1-kpk.pdf|Download PDF ~ ch10-trigon
- 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
- Question 2(i, ii, iii, iv and v) Exercise 8.3 @math-11-nbf:sol:unit08
- tan. =====Question 2(i)===== Rewrite the sum or difference as a product of two function: $\sin 70^{\circ} + ... OOD =====Question 2(ii)===== Rewrite the sum or difference as a product of two function: $\sin 76^{\circ} - ... n*} =====Question 2(iii)===== Rewrite the sum or difference as a product of two function: $\cos 58^{\circ} + ... gn*} =====Question 2(iv)===== Rewrite the sum or difference as a product of two function: $\cos \frac{p-q}{2}
- Atiq ur Rehman, PhD
- rg>, <[email protected]> **Field of Research:** Difference and functional equations, Real functions, Inequal... 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, ... Rehman, On Logarithmic Convexity for Giaccardi's Difference, Rad HAZU 515 (2013), 1–10. 10. J. Pečarić, Atiq
- Question 1(i, ii, iii & iv) Exercise 8.3 @math-11-nbf:sol:unit08
- e the product-to-sum formula to change the sum or difference: $$4 \sin 16x \cos 10x $$ ** Solution. ** \beg... e the product-to-sum formula to change the sum or difference: $10 \cos 10y \cos 6y$. ** Solution. ** \begin{... e the product-to-sum formula to change the sum or difference: $2 \cos5t \sin 3t$. ** Solution. ** \begin{doc... e the product-to-sum formula to change the sum or difference: $6\cos 5x \sin 10x$. ** Solution. ** \begin{al
- Question 1(v, vi, vii & viii) Exercise 8.3 @math-11-nbf:sol:unit08
- e the product-to-sum formula to change the sum or difference: $ \sin(-u) \sin 5u$. ** Solution. ** \begin{al... e the product-to-sum formula to change the sum or difference: $-2 \sin 100^{\circ}\sin (-20^{\circ}) $. ** So... e the product-to-sum formula to change the sum or difference: $\cos 23^{\circ} \sin 17^{\circ}$. ** Solution.... e the product-to-sum formula to change the sum or difference: $2 \cos56^{\circ} \sin48^{\circ}$. ** Solution.
- FSc Part 1 (KPK Boards) @fsc
- = Chapter 10: Trigonometric Identities of Sum and Difference of Angles ===== === Objectives === After reading ... c_part_1:ch10-trigonometric-identities-of-sum-and-difference-of-angles-fsc1-kpk.pdf|Download PDF}}** | **[[:f... 1:chapter 10 trigonometric identities of sum and difference of angles|Online view]]** </callout> ===== Chapt
- Question 1(ix, x & xi) Exercise 8.3 @math-11-nbf:sol:unit08
- e the product-to-sum formula to change the sum or difference: $2 \sin 75{\circ} \sin 15{\circ}$. ** Solution.... e the product-to-sum formula to change the sum or difference: $4 \sin \frac{u+v}{2} \cos \frac{u-v}{2} $. ** ... e the product-to-sum formula to change the sum or difference: $2 \cos \frac{2u+2v}{2}\sin \frac{2u-2v}{2} $.
- FSc Part 2 (KPK Boards) @fsc
- n and the statement of theorems on limits of sum, difference, product and quotient of functions. * evaluate ... ultiple of a function, the derivative of a sum or difference of two functions, the derivative of the product o
- B-Course of Mathematics (Paper A & B) @bsc:paper_pattern:sargodha_university
- , Newton - Raphson method and fixed point method. Difference operators. Interpolation (Newton’s and Lagrange’s... on methodFixed point method| |Numerical Analysis |Difference operators| |Numerical Analysis |Interpolation (Ne