Question

if cot theta=4/3 evaluate 4sin theta + 3cos theta /4sin theta - 3cos theta

Answer 1

Answer:

is in attachment

Step-by-step explanation:

it is in attachment

Answer 2

Given:

cot∅=4/3

To find:

4 sin∅ + 3cos∅

_______________......................[1]

4sin∅ - 3cos∅

We know that,

cot X= Adjacent side/Opposite Side

Thus,

cot∅=4/3

→A/O=4/3

→A=4 and O=3

By Pythagoras theorm,

H²=A²+O²

=4²+3²

=25

→H=5

We know that,

sin X=Opposite Side/Hypotenuse

and cosX= Adjacent side/Hypotenuse

Here,

sin∅=3/5 and cos∅=4/5

Substituting appropriate values in [1],

$\sf{ \frac{4 \times \frac{3}{5} + 3 \times \frac{4}{5} }{4 \times \frac{3}{5} - 3 \times \frac{4}{5} } } \\ \\ = \frac{ \frac{</p><p>12}{5} + \frac{12}{5} }{ \frac{12}{5} - \frac{12}{5} } \\ \\ = \frac{ \frac{24}{5} }{ \frac{0}{5} } \\ \\ = \boxed{ \frac{25}{0} }$

The value of given expression would be 25/0