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- 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 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.
- 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
- Question 5 and 6 Exercise 4.2 @math-11-kpk:sol:unit04
- }}\right)\\ &=\log b. \end{align} We see that the difference of consecutive terms $d$ is constant, i.e. indepe
- Question 7 Exercise 4.2 @math-11-kpk:sol:unit04
- ion==== Let $a_1$ be first term and $d$ be common difference of A.P. As given \begin{align} &a_6+a_4=6 \\ \im
- Question 7 & 8 Exercise 4.3 @math-11-kpk:sol:unit04
- equence\\ with first term $a_1=1$, and the common difference $d=2$.\\ We know that: \begin{align}S_n&=\dfrac{n
- Question 3 Exercise 5.3 @math-11-kpk:sol:unit05
- +40+\ldots$ ====Solution==== We use the method of difference as: \begin{align} & a_2-a_1=10-4=6 \\ & a_3-a_2=1
- Question 1, Exercise 10.1 @math-11-kpk:sol:unit10
- 1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 2, Exercise 10.1 @math-11-kpk:sol:unit10
- 1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 3, Exercise 10.1 @math-11-kpk:sol:unit10
- 1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question, Exercise 10.1 @math-11-kpk:sol:unit10
- 1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 5, Exercise 10.1 @math-11-kpk:sol:unit10
- 1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat
- Question 6, Exercise 10.1 @math-11-kpk:sol:unit10
- 1 of Unit 10: Trigonometric Identities of Sum and Difference of Angles. This is unit of A Textbook of Mathemat