Math, asked by Namya1209, 10 months ago

Find the general solution cosec X= cot X +√3​

Answers

Answered by anu24239
3

ANSWER....

AS YOU SEE SUCH QUESTION THAN I RECOMMEND YOU TO CONVERT SUCH QUESTION INTO SINE OR COSINE FORM SO THAT PARTICULAR QUESTION BECOME MORE FAMILIAR THAN THE BEFORE......°°^°°^^

 \frac{1}{ \sin \alpha  }  =  \frac{ \cos \alpha  }{ \sin \alpha  }  +  \sqrt{3}  \\  \\ multiply \: whole \: eq \: by \: sin \alpha  \\  \\ 1 =  \cos \alpha   +  \sin \alpha  \sqrt{3}  \\  \\ 1 -  \cos \alpha  =  \sin \alpha  \sqrt{3}  \\  \\ squaring \: on \: both \: side..... \\  \\ 1 +  {cos}^{2}  \alpha  - 2 \cos \alpha  = 3 {sin}^{2}  \alpha  \\  \\ convert \: sin \: \alpha  \: to \: cos \:  \alpha  \\  \\ 1 +  {cos}^{2}  \alpha  - 2 \cos \alpha  = 3(1 -  {cos}^{2}  \alpha ) \\  \\ 1 +  {cos}^{2}  \alpha  - 2 \cos \alpha  = 3 - 3 {cos}^{2}  \alpha  \\  \\ 1 - 3 + 4 {cos}^{2}  \alpha  - 2 \cos \alpha  = 0 \\  \\  - 2 + 4 {cos}^{2}  \alpha  - 2 \cos \alpha  = 0 \\  \\ 2 {cos}^{2}  \alpha  -  \cos \alpha  - 1 = 0 \\  \\ 2 {cos}^{2}  \alpha  - 2 \cos \alpha  +  \cos \alpha  - 1 = 0 \\  \\ (2 \cos \alpha  - 1)( \cos \alpha  - 1) = 0 \\  \\ first \: solution \\  \\  \cos \alpha  =  \frac{1}{2}  \\  \\  \cos \alpha  =  \cos \frac{\pi}{3}  \\  \\  \alpha  = 2n\pi +  \frac{\pi}{3}  \: or \: 2n\pi -  \frac{\pi}{3}  \\  \\ second \: solution \\  \\ cos \alpha  = 1 \\  \\ cos \alpha  = cos \: 0 \\  \\ x = 2n\pi

#BTSKINGDOM

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