Question

plzz ans it with step by step explanation​

Answer 1

Hey Pretty Stranger!

Here we're given with

$\sf \: \sin\theta + \cosec \theta = 2$

We can write it as

$\longrightarrow \sf \: \sin \theta + \dfrac{1}{ \sin \theta} = 2$

Squaring both the sides

$\longrightarrow \sf \: (\sin \theta + \dfrac{1}{ \sin \theta} ) ^{2} =( {2})^{2}$

$\longrightarrow \sf \: {sin}^{2} \theta+ \dfrac{1}{ {sin}^{2} \theta } + 2( \sin \theta)( \dfrac{1}{ \sin \theta} ) = 4$

$\longrightarrow \sf \: {sin}^{2} \theta+ \dfrac{1}{ {sin}^{2} \theta } + 2 = 4$

$\longrightarrow \sf \: {sin}^{2} \theta+ \dfrac{1}{ {sin}^{2} \theta } = 4 - 2$

$\longrightarrow \sf \: {sin}^{2} \theta+ \dfrac{1}{ {sin}^{2} \theta } = 2$

$\longrightarrow \sf \: {sin}^{2} \theta+ \cosec^{2} \theta = 2$

$\therefore$ Option 3) is the required answer.