Question

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

Answer 1

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