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Calculate tgα if:2cos2α+4√3sinα=5    α(π /2; π )

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Calculate tgα if:2cos2α+4√3sinα=5    α(π /2; π )

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`we have`

`2cos(2alpha)+4sqrt(3)sin(alpha)=5`   (i)

we know


Thus (i) reduces to

`2(1-2sin^2(alpha))+4sqrt(3)sin(alpha)=5`    (ii)

Let us assume `sin(alpha)=t` ,so above equation reduces to




Also we know






t=1.366 is not possible because `-1<=sin(alpha)<=1`




`alpha=158.53^o in(pi/2,pi)`

`` Ans.

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