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If cos(x-y),cosxa n d"cos"(x+y) are in H...

If `cos(x-y),cosxa n d"cos"(x+y)` are in H.P., then `cosxsec(y/2)=`

Text Solution

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The correct Answer is:
`+- sqrt2`
Since, `cos (x -y), cos x and cos (x +y)` are in HP
`:. cos x = (2 cos (x -y) cos (x +y))/(cos (x -y) + cos (x +y))`
`rArr cos x (2 cos x.cos y) = 2{cos^(2) x - sin^(2) y}`
`rArr cos^(2) x. cosy = cos^(2) x - sin^(2) y`
`rArr cos^(2) x.2sin^(2).(y)/(2) = 4 sin^(2).(y)/(2). cos^(2)/(y)/(2)`
`rArr cos^(2)x.sec^(2).(y)/(2) = 2`
`:. cos x. sec.(y)/(2) = +- sqrt2`
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