यदि `7sin^(2)theta+3cos^(2)theta=4,(0^(@) le theta le 90^(@))` है `theta` तो का मान ज्ञात करे?

Options

A. `(pi)/(2)`
B. `(pi)/(3)`
C. `(pi)/(6)`
D. `(pi)/(4)`

Answer

c

Explanation

`7sin^(2)theta+3cos^(2)theta=4`
`rArr7sin^(2)theta+3(1-sin^(2)theta)=4`
`rArr7sin^(2)theta+3-3sin^(2)theta=4`
`rArr 4sin^(2)theta=1`
`rArrsin^(2)theta=(1)/(4)rArrsin theta=(1)/(2)=sin30^(@)`
`theta=30^(@)=(pi)/(6) [therefore pi^(2)=180^(@)]`