Question

prove that cosec2-cot2=1​

Answer 1

Hey mate here is your answer

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I am putting the value of 1=Cos2+Sin2

Answer 2

$\huge {Solution }$

To prove :

${ \csc }^{2} - { \cot }^{2} = 1$

Proof :

As we know that

$\csc = \frac{1}{ \sin }$

$= > { \csc }^{2} = \frac{1}{ { \sin}^{2} }$

and

$\cot = \frac{ \cos }{ \sin}$

$= > { \cot }^{2} = \frac{ { \cos}^{2} }{ { \sin }^{2} }$

Then,

$= > \frac{1}{ { \sin }^{2} } - \frac{ { \cos }^{2} }{ { \sin }^{2} }$

$= > \frac{(1 - { \cos }^{2} )}{ { \sin}^{2} }$

$= > \frac{ { \sin }^{2} }{ { \sin }^{2} }$

$= > 1$