Question

Show that, sin^2 0 (1 + cot^2 0) = 1​

Answer 1

Hello Mate,

To Prove:

${ \sin}^{2} \alpha \: (1 + { \csc }^{2} \alpha ) = 1$

$\huge{\blue{\star}} {\red{\huge{\mathfrak{Solution}}} [tex] \huge{\blue{\star}}</p><p></p><p></p><p>We know, </p><p></p><p>[tex] { \csc }^{2} \alpha - { \cot }^{2} \alpha = 1 \\ \\ { \csc }^{2} \alpha = 1 + { \cot }^{2} \alpha$

Now subsitiute the cosecant value in the above question we get,

${ \sin }^{2} \alpha \times { \csc }^{2} \alpha = 1$

This is because cosecant is a reciprocal of sine,

${ \sin}^{2} \alpha \times \frac{1}{ { \sin }^{2} \alpha } \\ \\ = 1$

Hope it helps:)