If `2sin^(2)_(theta)-3sinta_(theta)+1=0` `theta` being positive angle, then the value of `theta` are (यदि धन न्यूनं कोण है तो `theta` के मान है)

Options

A. `30^(@),90^(@)`
B. `60^(@),55^(@)`
C. `60^(@),45^(@)`
D. `45^(@),60^(@)`

Answer

a

Explanation

According to the question.
`2sin^(2)theta-3sintheta+1=0`
Put `theta=30^(@)`
`2xx sin^(2)30^(@)-3sin30^(@)+1=0`
Let ` theta=30^(@)`
`rArr4xxsin^(2)30^(@)-1=0`
`rArr4xx(1)/(4)-1=0`
`rArr0=0` satisfied
`rArr` In the question ,putting `theta=30^(@)`
`rArrcos^(2)theta+tan^(2)theta`
`rArrcos^(2)30^(@)+ tan^(2)30^(@)`
`rArr ((sqrt3)/(2))^(2)+((1)/sqrt(3))^(2)`
`rArr(3)/(4)+(1)/(3)rArr(13)/(12)`