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If sin^(-1)x+2cos^(-1)x=(2pi)/3, then fi...

If `sin^(-1)x+2cos^(-1)x=(2pi)/3`, then find x.

Text Solution

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`sin^(-1)x+2cos^(-1)x=(2pi)/3`
`rArrsin^(-1)x+cos^(-1)x+cos^(-1)x=(2pi)/3`
`rArr pi/2+cos^(-1)x=(2pi)/3`
`rArr cos^(-1)x=pi/6`
`:' cos^(-1)x" lie in "[0,pi]`
`:. Cos^(-1)x=pi/6`
`rArr x=sqrt3/2`
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