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Maths-

General

Easy

Question

$text If end text t a n invisible function application m theta plus c o t invisible function application n theta equals 0 comma$ then the general value of $theta$ is

$\frac{(2 r + 1) π}{2 (m - n)}$
$\frac{(2 r + 1) π}{2 (m + n)}$
$\frac{r π}{m + n}$
$\frac{r π}{m - n}$

The correct answer is: $fraction numerator left parenthesis 2 r plus 1 right parenthesis pi over denominator 2 left parenthesis m minus n right parenthesis end fraction$

The given equation can be written as
$tan invisible function application m theta equals negative cot invisible function application n theta equals tan invisible function application open parentheses fraction numerator pi over denominator 2 end fraction plus n theta close parentheses$
$text Therefore, end text$
$m theta equals r pi plus open parentheses fraction numerator pi over denominator 2 end fraction plus n theta close parentheses comma r element of 1$
$rightwards double arrow open parentheses m minus n close parentheses theta equals fraction numerator 1 over denominator 2 end fraction open parentheses 2 r plus 1 close parentheses pi comma r element of I$
$table row cell text end text text S end text text o end text text , end text text end text end cell row cell theta equals fraction numerator left parenthesis 2 r plus 1 right parenthesis pi over denominator 2 left parenthesis m minus n right parenthesis end fraction comma r element of ∣ end cell end table$

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