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 does not hold?

Answer»

`sin(beta+gamma)=sin(alpha+delta)`
`sin(beta-gamma)=sin(alpha-delta)`
`tan2(alpha+beta)=tan(beta+delta)`
`cos(alpha+gamma)=cos2beta`

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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