Question

If cosec theta minus cot theta is equal to 1 by 4 then cosec theta + cot theta is equal to

Answer 1

❏Question :-

$\sf if \csc \theta - \cot \theta = \frac{1}{4} \: then \: find \: the \\ \sf value \: of \csc \theta + \cot \theta$

❏Answer :-

$\large \: \boxed{\to \csc \theta + \cot \theta = 4} \:$

❏Formula used :-

$\sf \: Here \: we \: will \: use \: trigonometric \: identity \\ \leadsto \: { \csc}^{2} \theta - { \cot}^{2} \theta = 1 \\ \bf and \\ \leadsto \bf {x}^{2} - {y}^{2} = (x + y)(x - y)$

❏Solution :-

Given that

$\to \: \csc \theta - \cot \theta = \frac{1}{4} \\ \bf \: we \: know \: that \\ \\ \to \: { \csc}^{2} \theta - { \cot}^{2} \theta = 1 \\ \\ \because \bf {x}^{2} - { y }^{2} = (x + y)(x - y) \: \\ \therefore \\ \to \sf ( \csc \theta + \cot \theta)( \csc \theta - \cot \theta) = 1 \\ \because \: \csc \theta - \cot \theta = \frac{1}{4} \\ \therefore \\ \to \sf ( \csc \theta + \cot \theta) \times \frac{1}{4} = 1 \\ \\ \boxed{\to \csc \theta + \cot \theta = 4}$