Math, asked by heyimgauravpatel, 2 months ago

cotπ = √2+1
then find the value of cosecπ secπ​

Answers

Answered by richapariya121pe22ey
1

Step-by-step explanation:

  \cot(\pi)  =  \sqrt{2}  + 1 \\ 1 +  { \cot }^{2} x =  { \cosec}^{2} x \\ 1 +  {( \sqrt{2}) }^{2}  =  { \cosec }^{2} \pi \\   { \cosec }^{2} \pi = 1 + 2 = 3 \\  \cosec(\pi)  =  \sqrt{3}  \\  \\  \cosec(\pi)  =  \frac{1}{ \sin(\pi) }  \\  \sin(\pi)  =  \frac{1}{ \cosec(\pi) }  =  \frac{1}{ \sqrt{3} }  \\  { \sin}^{2} \pi +   { \cos }^{2} \pi = 1 \\  { \cos }^{2} \pi = 1  -  { \sin}^{2} \pi = 1 -  { (\frac{1}{ \sqrt{3} }) }^{2}  = 1 -  \frac{1}{3}  =  \frac{2}{3}  \\  \cos(\pi)  =  \sqrt{ \frac{2}{3} }  \\  \cos(\pi)  =  \frac{1}{ \sec(\pi) }  \\  \sec(\pi)  =  \frac{1}{ \cos(\pi) }  =  \frac{1}{ \sqrt{ \frac{2}{ 3} } }  =  \sqrt{ \frac{3}{2} }

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