Question

How to solve this By L.H.S ​

Answer 1

Step-by-step explanation:

hence proved L.H.S is equal to R.H.S

Answer 2

Given :-

$\rm \: \dfrac{tan \theta}{ {sin}^{2} \theta } = sec \theta \:cosec\theta$

To prove :-

L.H.S = R.H.S

Proof :

$\rm \: R.H.S = sec \theta \:cosec\theta$

$\rm \longrightarrow L.H.S =\dfrac{tan \theta}{ {sin}^{2} \theta } \\ \\ \\ \rm \longrightarrow tan \theta\times\dfrac{1}{ {sin}^{2} \theta } \\ \\ \\ \rm \: we \: know \: that \: : \rightarrow \: tan \: x = \frac{sin \:x}{cos \:x}\\ \\ \\ \rm \longrightarrow \frac{sin \: \theta}{cos \: \theta} \times\dfrac{1}{ {sin}^{2} \theta } \\ \\ \\ \rm \longrightarrow \dfrac{1}{cos \: \theta} \times\dfrac{1}{ {sin}\theta } \\ \\ \\ \rm \: we \: know \: that \rightarrow\dfrac{1}{cos \: x} = sec \: x \: \: and \: \: \dfrac{1}{s in\: x} = cosec \: x \\ \\ \\ \rm \longrightarrow {sec \: \theta} \times{ cosec \theta } \\ \\ \\ \rm \longrightarrow {sec \: \theta} \: { cosec \theta }$

Therefore, L.H.S = R.H.S

Hence proved