If `|sin x+cos x|=|sin x|+|cos x|` then `x` lies in `1`) `1^(st)` quadrant only `2`) `1^(st)` and `3^(rd)` quadrant `3`) `4^(th)` quadrant only `4`) `3^(rd)` quadrant only

Answer

`atoq;btoq;ctop,r;dtop,s`

Explanation

a. Since angles A,B and C are acute angles, we have
`A+Bgtpi//2`
`Agtpi/2-B`
`rArr sinA-cosBgt0`
`rArr cosB-sinAlt0 ...(i)`
Again, `Bgtpi/2-A`
`sinBgtcosA`
`sinB-cosAgt0 …(ii)`
From Eqs. (i) and (ii), we get that x-coordinate is -ve and y-coordinate is +ve.
therefore, point is in 2nd quadrant only.
b. `2^sinthetagt1rArr sinthetagt0`
`rArr thetain1st`or 2nd quadrant
`3^costhetalt1rArr costhetalt0`
`rArrthetain2ndor 3rd` quadrant
Hence,` thetain 2nd` quadrant
c. `abs(cosx+sinx)=abssinx+abscosx`
Thus, cosx and sinx must have same sign or at least one is zero.
d. `L.H.S. =(1-sinA)/abscosA+sinA/cosA=1/cosA`,
which is true only if `abscosA=cosA`