Question

Solve this question LHS=RHS

Answer 1

$\frac{ {cos}^{2}0 }{sin0} - cosec0 + sin0 = 0 \\ \frac{1 - {sin}^{2}0}{sin0} - \frac{1}{sin0} + \frac{ {sin}^{2}0 }{sin0} \\ \frac{1 - {sin}^{2}0 - 1 + {sin}^{2}0 }{sin0} \\ \frac{0}{sin0} \\ 0$
LHS = RHS

Hence proved

Answer 2

$\red {\bold {\underline {\underline {\star \: {Given}}}}}$

$\frac{ \cos \phi }{ \sin\phi } - \cosec\phi + \sin \phi = 0.$

$\red {\bold {\underline {\underline {\star \: {Answer}}}}}$

Let's Try to Prove LHS = RHS.

Taking LHS__________

$\implies \frac{ { \cos} ^{2} \phi }{ \sin \phi} - \cosec \phi + \sin \phi \\ \\ \implies \: \frac{ { \cos} ^{2} \phi }{ \sin \phi} - \frac{1}{ \sin\phi} + \sin \phi \\ \\ \implies \frac{ { \cos }^{2} \phi - 1 + { \sin }^{2} \phi}{ \sin \phi} \\ \\ \implies \: \frac{ \cancel { \cos }^{2} \phi - \cancel 1 + \cancel1 - \cancel{ \cos}^{2} \phi }{ \sin \phi} \\ \\ \implies \: 0.$