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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 |
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Answer» `400^@ltthetalt580^@` `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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