Question

Prove 1+ 1/cot²=1/cos²​

Answer 1

Answer:

LHS:

(cot2 + 1)/cot2

cosec2/cot2

(cosec/cot)2

(1|sin/cos|sin)2

(1/cos)2

1/cos2

therefore, LHS=RHS

Hence proved.

Answer 2

Answer:

$1 + \frac{1}{ \cot {}^{2} } = \frac{1}{ \cos {}^{2} }$

using cot = cos/sin

$1 + \frac{ \sin {}^{2} }{ \cos{}^{2} } = \frac{1}{ \cos{}^{2} }$

$\frac{ \cos {}^{2} + \sin {}^{2} }{ \cos {}^{2} } = \frac{1}{ \cos {}^{2} }$

using cos² + sin² = 1

$\frac{1}{ \cos {}^{2} } = \frac{1}{ \cos {}^{2} }$

LHS = RHS

hence proved.