`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. Which of the following holds?A. `cos(alpha-delta)gt0`B. `cos(alpha-delta)=0`C. `cos(alpha-delta)lt0`D. `cos(alpha-delta)gt0or `cos(alpha-delta)lt0`

`alpha,beta,gammaand delta` are angles in I,II,II and IV quadrants, re

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. Which of the following holds?A. `cos(alpha-delta)gt0`B. `cos(alpha-delta)=0`C. `cos(alpha-delta)lt0`D. `cos(alpha-delta)gt0or `cos(alpha-delta)lt0`
Answer» Correct Answer - A `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 d is 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^@`