Question

Given 4 cot a=3 find
1) sin a
2 sec a
3 cosec²a-cot² a

Answer 1

cot a = 3/4

1) sin a = 4/5

2) sec a= 5/3

3) cosec^a - cot^a = 1

Answer 2

$4 \: cot = 3 \\ cot \: a = \frac{3x}{4x } \\ \color{magenta}\text{considre right - \: angle triangle} \\ \\ cot \: a = \frac{base}{prendicular} = \frac{ab}{bc} \\ \\ let \: ab = 3x \: units \\ and \: bc = 4x \: units \\ \\ \color{skyblue}\text{by \: pythagoras \: theorem} \\ \\ </p><h2>(i)Sin A</h2><p>[tex] \frac{p}{h} = \frac{5}{4}$

(ii)Sec A

$\frac{h}{b} = \frac{5}{3}$

(iii)Cosec² A-Cot² A

$(\frac{5}{4 })^{2} - (\frac{3}{4} )^{2} \\ \\ = \frac{25}{16} - \frac{9}{16} \\ \\ = \frac{16}{16} = 1$