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Linear Inequations

Given A= x:-1...

Question

Given $A = {x : - 1 < x \leq 5, x \in R} a n d B = {x : - 4 \leq x < 3, x \in R}$

Represent on different number lines :

(i) $A \cap B$ (ii) $A^{'} \cap B$ (iii) $A - B$

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A = {x : - 2 < x \leq 5, x \in R}

{x : - 5 \leq x < 3, x \in R}

U = {x : - 5 \leq x \leq 5}

A \cap B

A^{'} \cap B

on different number lines.

A = {x : - 1 < x \leq - 5, x \in R}

B = {x : - 4 < x \leq 3, x \in R}

Represent on different number lines:
(i)

A \cap B

A^{'} \cap B

A - B

A = {x : - 1 \leq x \leq 4, x ϵ R}

B = {x : - 4 \leq x < 2, x ε R}

A \cap B

A^{'} \cap B

on the number line.
[4 MARKS]

Q. Prove that:

(i)

\frac{1}{\sin (x - a) \sin (x - b)} = \frac{\cot (x - a) - \cot (x - b)}{\sin (a - b)}

\frac{1}{\sin (x - a) \cos (x - b)} = \frac{\cot (x - a) + \tan (x - b)}{\cos (a - b)}

\frac{1}{\cos (x - a) \cos (a - b)} = \frac{\tan (x - b) - \tan (x - a)}{\sin (a - b)}

Q. Solve the following inequation and write the solution set :

13 x - 5 < 15 x + 4 < 7 x + 12, x ϵ R

Represent the solution on a real number line.
[3 MARKS]

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