Question

about ye solve kro.....
dekhe kisme kitna hai dum❤

correctly answer it an I will be marking it as brainliest to the one who solves all of them.........❤❤​

Answer 1

(1) Factorisation

${a}^{2} {b}^{2} {x}^{2} + {b}^{2} x - {a}^{2} x - 1 \\ \\ = {b}^{2} x ({a}^{2} x + 1) - 1( {a}^{2} x + 1) \\ \\ = ( {a}^{2} x + 1)( {b}^{2} x - 1)$

(2) Distance between points (2, -2) and (-1, x) is 5 units.

$= > \sqrt{ {(2 + 1)}^{2} +{ (x + 2) }^{2} } = 5 \\ \\ = > {3}^{2} + {(x + 2)}^{2} = {5}^{2} \\ \\ = > {(x + 2)}^{2} = 25 - 9 \\ \\ = > {(x + 2)}^{2} = 16 = {4}^{2} \\ \\ = > x + 2 = 4 \\ \\ = > x = 4 - 2 \\ \\ = > x = 2$

(3) Trignometry

$\frac{2}{3} { \csc }^{2} 58 - \frac{2}{3} \cot(58) \tan(32) - \frac{5}{3} \tan(13) \tan(37) \tan(45) \tan(53) \tan(77) \\ \\ = \frac{2}{3} { \csc }^{2} 58 - \frac{2}{3} \tan(32) \tan(32) - \frac{5}{3} \tan(37) \cot(37) \cot(77) \tan(77) \times 1 \\ \\ = \frac{2}{3} { \csc }^{2} 58 - \frac{2}{3} { \tan }^{2} 32 - \frac{5}{3} \times 1 \times 1 \times 1 \\ \\ = \frac{2}{3} ( { \csc }^{2} 58 - { \cot}^{2} 58) - \frac{5}{3} \\ \\ = \frac{2}{3} \times 1 - \frac{5}{3} \\ \\ = \frac{2 - 5}{3} \\ \\ = - \frac{3}{3} \\ \\ = - 1$