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If cos theta - sin theta = (1)/(5), wher...

If `cos theta - sin theta = (1)/(5)`, where `0 lt theta lt (pi)/(4)`, then

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The correct Answer is:
`a to q; b to r; c to s; d to p`
`cos theta - sin theta = (1)/(5)`, where `0 lt theta lt (pi)/(2)" "` ...(i)
Squaring both sides of Eq. (i), we get
`1-sin2theta = (1)/(25)`
`or " " sin 2theta = (24)/(25)`
`or " " cos 2theta = (7)/(25)`
Also, `(cos theta + sin theta)^(2) = (cos theta - sin theta )^(2) + 4 cos theta sin theta `
`= (1)/(25) + 2 sin 2theta = (1)/(25) + (48)/(25) = (49)/(25)`
`rArr cos theta + sin theta = (7)/(5)" "`...(ii)
or `" "((cos theta + sin theta))/(2) = (7)/(10)`
Also solving Eqs. (i) and (ii), we geet `cos theta = 4//5`.
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