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Match the following Column I to Column I...

Match the following Column I to Column II

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The correct Answer is:
`atoq;btoq;ctop,r;dtop,s`
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`
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