If$$cos^2(x)$$​ + sin x = 5/4, then find the value of ‘sin x’

Correct option is D

Given:

cos^2(x) + sin x = 5\4

Formula Used:

​$$cos^2(x) =1-sin^2(x)\\a^2 +b^2 - 2ab=(a-b)^2$$​​

Solution:

​$$cos^2(x) + sin x = \frac54\\1-sin^2(x) +sin x =\frac54$$​​

​$$let sin x = t\\t^2-t +\frac54 -\frac14 =0\\t^2 -t + \frac14 =0\\4t^2-4t+1=0\\(2t-1)=0\\t=\frac12\\sin x =\frac12\\so, x= 30\degree$$​​