यदि `tan^(2)alpha=1+2tan^(2)beta(alpha,beta` एक धनात्मक न्यूनकोण है तो `sqrt(2)cosalpha-cosbeta` किसके बराबर है?

Options

A. 0
B. `sqrt(2)`
C. `1`
D. `-1`

Answer

a

Explanation

`tan^(2)alpha=1+2tan^(2)beta`
`rArrsec^(2)alpha-1=1+2(sec^(2)beta-1)`
`rArrsec^(2)alpha-1= 2sec^(2)beta-1`
`rArr(1)/(cos^(2)alpha)=(2)/(cos^(2)beta)`
`sqrt(2)cos alpha-cos beta=0`
Alterante
`tan^(2)alpha=1+2tan^(2)beta`
Put `beta=45^(@)`
`tan^(2)alpha=1+2 tan^(2)45^ (@)`
`tan^(2)alpha=3`
`tanalpha=sqrt(3)`
`alpha=60^(@)`
Put `alpha =60^(@).beta=45^(@)`
`=sqrt(2)cos alpha=cosbeta=sqrt(2)cos60^(@)-cos45^(@)`
`=sqrt(2)xx(1)/(2)-(1)/sqrt(2)=(1)/sqrt(2)-(1)/sqrt(2)=0`