1.

alpha,beta,gammaand delta are angles in I,II,II and IV quadrants, respectively and none of them is an integral multiple of pi//2. They form an increasing arithmetic progression.if alpha+beta+gamma+delta=thetaand alpha70^@, then

Answer»

`400^@ltthetalt580^@`
`470^@ltthetalt650^@`
`680^@ltthetalt860^@`
`540^@ltthetalt900^@`

Solution :`0ltalphalt90^@,90^@ltbetalt180^@`
`180^@ltgammalt270^@,270^@ltdeltalt360^@`
`rArrgammalt270^@ltalpha+deltalt450^@`
`rArr alpha+delta` lies in the I or IV quadrant and cosine in both is positive.
If dis the common RATIO of theA.P., then
`beta=alpha+d,gamma=alpha+2d,delta=alpha+3d`
`rArr beta+gamma=alpha+delta,2(alpha-beta)=-2d=beta-delta`
`and alpha+gamma=2beta`,
Now, `beta-gamma=-d,alpha-delta=-3d`
`270^@ltdeltalt360^@`
`rArr 270^@ltalpha+3dlt360^@`
`rArr 200^@lt3dlt290^@( :. alpha=70^@)`
`rArr400^@lt+6d,580^@`
`rArr 680^@lt4alpha+6dlt860^@`
`680^@ lttheta lt 860^@`


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