Question

Cosec theta = 13 / 12 find cot theta - tan theta ​

Answer 1

QUESTION:

Cosec theta = 13 / 12 find cot theta - tan theta

ANSWER:

$\\ \\ \\ \\ we \: \: know \: \: that \\ \\ \\ cotθ = \sqrt{ {cosec}^{2}θ - 1 } \\ \\ \\ cotθ = \sqrt{ { \frac{(13)}{(12)} }^{2} } - 1 \\ \\ \\ cotθ = \sqrt{ \frac{169 - 144}{144} } \\ \\ \\ cotθ = \sqrt{ \frac{25}{144} } \\ \\ \\ cotθ = \frac{5}{12} \: \: \: \: - - - (answer) \\ \\ \\ \\ \\ \\ now : \\ \\ \\ we \: \: know \: \: that \: \: \\ \\ \\ tanθ = \frac{1}{cotθ} \\ \\ \\ hence \: \: \: tanθ= \frac{12}{5} \\ \\ \\ now \: \: to \: \: find : \\ \\ \\ cotθ - tanθ \\ \\ \\ = \frac{5}{12} - \frac{12}{5} \\ \\ \\ = \frac{25 - 144}{60} \\ \\ \\ = \frac{ - 119}{60} \: \: \: \: answer$