Question

prove the following identities

cosø . cosecø = cotø​

Answer 1

$\huge \sf {\orange {\underline {\pink{\underline❥ {A᭄ɴsᴡᴇʀ࿐ \ :- }}}}}$

$\green{To \: Prove: \: cos \: \theta \: . \: cosec \: \theta = cot \: \theta}$

$L.H.S. = cos \: \theta . cosec \: \theta$

$= cos \: \theta × \large {\frac{1}{sin \: \theta}} \: (\because \: \small{cosec \: \theta} = \large \frac{1}{sin \: \theta})$

$= \large \frac{cos \: \theta}{sin \: \theta}$

$= cot \: \theta = R.H.S.$

$\therefore \: cos \: \theta \: . \: cosec \: \theta = cot \: \theta$

$\blue {\bf{Hence \: proved \: that, cos \: \theta . cosec \: \theta = cot \: \theta}}$