Find the least positive value of theta for which cot(5*theta-10*) = ....

[simeoncalixte]

Question: Find the least positive value of \(\displaystyle \theta\) for which:

. . . . .\(\displaystyle \cot\left(5\theta\, -\, 10^{\circ}\right)\, =\, \dfrac{1}{\tan\left(4\theta\, -\, 3^{\circ}\right)}\)

Explain steps as well if possible been at this for a day now test tomorrow..

FOIL
\(\displaystyle \dfrac{5\theta\, -\, 10^{\circ}}{1}\, =\, \dfrac{1}{4\theta\, -\, 3^{\circ}}\)

\(\displaystyle \dfrac{\left(5\theta\, -\, 10^{\circ}\right)\left(4\theta\, -\, 3^{\circ}\right)}{1\left(4\theta\, -\, 3^{\circ}\right)}\, =\, \dfrac{1}{4\theta\, -\, 3^{\circ}}\)

\(\displaystyle \dfrac{20\theta\, -\, 5\theta(3^{\circ})\, -\, 4\theta(10^{\circ})\, +\, 30^{\circ}}{4\theta\, -\, 3^{\circ}}\, =\, \dfrac{1}{4\theta\, -\, 3^{\circ}}\)

\(\displaystyle 20\theta\, -\, \theta(7^{\circ})\, +\, 30^{\circ}\)

this is what i have done but it doesn't look right at all.. so please help

 

[Deleted member 4993]

Question: Find the least positive value of \(\displaystyle \theta\) for which:

. . . . .\(\displaystyle \cot\left(5\theta\, -\, 10^{\circ}\right)\, =\, \dfrac{1}{\tan\left(4\theta\, -\, 3^{\circ}\right)}\)
Explain steps as well if possible been at this for a day now test tomorrow..

this is what i have done but it doesn't look right at all.. so please help

You know:

\(\displaystyle \dfrac{1}{tan(\theta)} \ = \ cot(\theta)\)

then

\(\displaystyle \dfrac{1}{tan(4\theta - 3^o)} \ = \ ??\)

 

[simeoncalixte]

theta equals 7.... Feel very slow but thank you for all your help