If `sintheta-costheta=(7)/(13)` and `0^(@) lt theta lt 90^(@)`,
then the value of `sin_(theta)+cos_(theta)` is(यदि `sintheta-costheta=(7)/(13)and 0^(@)` और `0^(@) lt theta lt 90^(@)` तो का मान ज्ञात क्या होगा )

Options

A. `(17)/(13)`
B. `(13)/(17)`
C. `(1)/(13)`
D. `(1)/(17)`

Answer

a

Explanation

`sintheta -cos theta=(7)/(13)=alpha`
When
`ax+by=m` .....(i)
`bx- ay=n` ...........(ii)
By adding these two equations after making square on both sides we get
`(a ^(2)+b^(2))(x^(2)+y^(2))=m^(2)+n^(2)`
In the some process
`Sin theta+-Cos theta=a`
Then `Sin theta-+costheta=sqrt(2-a^(2))`
`sintheta+cos theta=sqrt(2-((7)/(13))^(2))`
`=sqrt(2-((49)/(169)))=sqrt((289)/(169))=(17)/(13)`