Question

If cot theta = 2, find the value of 2 sin theta - 3 cos they divided by 2 sin theta+ 3 cos theta

Answer 1

HEY

HERE IS ANSWER.

$\bf{answer = \frac{ - 1}{2} }$

$\bf{step \: by \: step \: explanation}$

Given: -

$cot \theta=2$


To find:-
$\frac{2 \sin \theta - 3cos \theta }{2sin \theta + 3cos \theta}$
pp

$cot \theta = \frac{2}{1}$
since

cot theta=b/p

means base upon perpendicular.

hence

base=2 units

perpendicular=1 units

so now

hypotenuse=

(h)^2=b^2+P^2

so

h^2=2^2+1^2

h^2=4+1

h^2=5

$h = \sqrt{5}$


so

$\sin \theta = \frac{perpendicular}{hypotenuse}$

$\sin \theta = \frac{1}{ \sqrt{5} }$
$\cos \theta = \frac{base}{hypotenuse}$

$\cos \theta = \frac{2}{ \sqrt{5} }$

so now

put value get result


please see in attachment.

HOPE IT HELPS

THANKS