यदि `costheta+sintheta=m` और `sectheta+co s ectheta=n` तो `n(m^(2)-1)` का मान किसके बराबर होगा?

Options

A. mn
B. 4mn
C. 2n
D. 2m

Answer

d

Explanation

According to question
`cos theta+sin theta=m`
`sec theta+co s ectheta=n`
Put `theta=45^(@)`
`cos45^(@)+sin45^(@)=m`
`sec45^(@)+co s ec45^(@)=n`
`(1)/sqrt(2)=m,sqrt(2)+sqrt(2)=n`
`m=sqrt(2),n=2sqrt(2)`
`thereforen(m^(2)-1)`
`=2sqrt(2)((sqrt(2))^(2)-1)`
`=2sqrt(2)(2-1)`
` =2sqrt(2)`
Now check from option only one option satisfy
2m=2`xxsqrt(2)`
`=2sqrt(2)`