If `cosx+cos^(2)x=1` , the numberical value of(यदि `cosx+cos^(2)x=1` है तो का अंकित मान क्या होगा )

Options

A. `-1`
B. 2
C. 0
D. 1

Answer

c

Explanation

`cos theta+sintheta=sqrt(2)cos theta`
Squaring both sides
`cos^(2)theta+sin^(2)theta+2cos thetasintheta=2cos^(2)theta`
`rArr 2cos^(2)theta-cos^(2)theta-sin^(2)theta=2`
`cos theta sintheta`
`rArrcos^(2)theta-sin^(20theta=2sin theta cos theta`
`rArr(cos theta-sin theta)(sqrt(2)cos theta)=`
`2sin theta.cos theta`
`rArr(cos theta-sin theta)=(2sinthetacos theta)/(sqrt(2costheta))`
Alternate Let `sqrt(2)cos theta=alpha`
`therefore cos theta+-sin theta=a`
`cos thea+-sintheta=sqrt(2-a^(2))`
`=sqrt(2(1-cos^(2)theta))`
`=sqrt(2sin^(2)theta)=sqrt(2)sin theta`