Question

Solve for x : 2 sin²x = 3 cos x​

Answer 1

Step-by-step explanation:

$2 {sin}^{2} x = 3cos \: x \\ \\ 2(1 - {cos}^{2} x) = 3cos \: x \: \\ \\ 2 - 2 {cos \: }^{2} x = 3cos \: x \\ \\ 2 = 3cos \: x \: + 2 {cos \: }^{2} x \\ \\ 2 {cos \: }^{2}x + 3cos \: x - 2 = 0 \\ \\ roots \: are..... \frac{ - b \binom{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \frac{ - 3 \binom{ + }{ - } \sqrt{9 + 16} }{4} \\ \\ \frac{ - 3 \binom{ + }{ - } \sqrt{ 25} }{4} \\ \\ \frac{ - 3 \binom{ + }{ - } 5}{4} \\ \\ \frac{ - 3 + 5}{4} ......... \frac{ - 3 - 5}{4} \\ \\ \frac{2}{4} ........ \frac{ - 8}{4} \\ \\ \frac{1}{2} ...... - 2..... \\ \\ so.....cos \: x \: = \frac{1}{2} \\ \\ x = 60$

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Answer 2

Answe............................. . ..............