यदि `2(cos^(2)theta-sin^(2)theta)=1,theta` है और धनात्मक न्यूनकोण है तो `theta` का मान ज्ञात करे?

Options

A. `60^(@)`
B. `30^(@)`
C. `45^(@)`
D. `22(1)/(2)`.

Answer

b

Explanation

`2 (cos^(2) theta-sin^(2)theta)=1`
`rArr cos^(2)theta -sin^(2)theta=(1)/(2)`
`rArr2sin^(2)theta=1-(1)/(2)`
`rArrsin^(2)theta=(1)/(2)`
`rArr sin theta=(1)/(2)=sin30^(@)`
Alternate
Take help from option
Let `theta=30^(@)`
`rArr2(cos^(2)theta-sin^(2)theta)=1`
`rArr2(cos^(2)30^(@)-sin^(2)30^(@))=1`
`=2[((sqrt(3))/(2))^(2)-((1)/(2))^(2)]=1`
`=2[(3)/(4)-(1)/(4)]=1`
`rArr2xx(2)/(4)=1`
`rArr1=1`