यदि `tantheta=(sinalpha+cosalpha)/(sinalpha+cosalpha)` है तो `sinalpha+cosalpha` का मान क्या होगा?

Options

A. `+-sqrt(2)sintheta`
B. `+-sqrt(2)costheta`
C. `+-(1)/(sqrt(2))sintheta`
D. `+-(1)/(sqrt(2))costheta`

Answer

b

Explanation

`tantheta=(sinalpha+cos alpha)/(sinalpha+cos alpha)`
`therefore` squaring both sides and after that add 1 both sides
`1+tan^(2)theta=1+((sin alpha-cosalpha)^(2))/((sinalpha+cos alpha)^(2))`
`sec^(2)theta=((sinalpha+cosalpha)^(2)+(sinalpha-cosalpha)^(2))/((sinalpha+cos alpha)^(2))`
`sec^(2)theta=(2(sin^(2)alpha+cos^(2)alpha))/((sinalpha+cosalpha)^(2))`
`(1)/(cos^(2)theta)=(2)/((sinalpha+cosalpha)^(2))`
`(1)/(costheta)=( +-sqrt(2))/(sinalpha+cos alpha)`
`sin alpha+cos alpha=+-sqrt(2)cos theta`