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Find the general solution of `cot x + tan x = 2 cosec x`

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We have, `cot x + tan x = 2 cosec x`
`therefore" "(cosx)/(sinx) +(sinx)/(cosx) = (2)/(sin x)`
`rArr" "(cos^(2)x +sin^(2)x)/(sin xcosx) = (2)/(sinx)`
`rArr " "(cos^(2)x + sinx^(2)x)/(sin x cos x) = (2)/(sinx)`
`rArr" "(1)/(sinx cos x) = (2)/(sinx)`
`rArr" "(1)/(cos x) = 2 " "(because sin x ne 0)`
`therefore" "cosx = (1)/(2)`
`rArr" "cosx = cos.(pi)/(2)`
The general solution of `cos theta = cos alpha ` is
`theta = 2npi pm alpha, n inZ`
Therefore, required general solution is
`x = 2npi pm (pi)/(3), n in Z`

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