यदि `theta` एक न्यूनकोण है और`7sin^(2)theta+3cos^(2)theta=4`, है तो `tantheta` का मान ज्ञात करे ?

Options

A. `sqrt(3)`
B. `(1)/(sqrt(3))`
C. `1`
D. `0`

Answer

b

Explanation

`7sin^(2)theta+3cos^(2)theta=4`
`7sin^(2)theta+3(1-sin^(2)theta)=4`
`7sin^(2)theta+3-3sin^(2)theta=4`
`4sin^(2)theta=1`
`sin theta=(1)/(4)rArrsintheta=(1)/(2)`
`sin theta=sin30^(@)`
`tan 30^(@)=(1)/sqrt(3)`
Alternate
Put `= 30^(@)`
`7xxsin^(2)30^(@)+3cos^(2)30^(@)=4`
`7xx(1)/(4)+3xx(3)/(4)=4`
`(7)/(4)+(9)/(4)=4`
`(16)/(4)=4`
`4=4` (satisfied)
`therefore tan 30^(@)=(1)/sqrt(3)`