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Solve the equation, 1+secx = 8tan^(2)(x/...

Solve the equation, `1+secx = 8tan^(2)(x/2)`

Text Solution

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Using `tan^(2)x/2= (1-cosx)/(1+cosx)` in the equation, we get
`1+secx=(8(1-cosx))/(1+cosx)`
`rArr (1+cosx)^(2) = 8cosx(1-cosx)`
`rArr cosx=1/3 = cos alpha` (say)
Then the general solution can be written as
`x=2npi +- alpha`
`=2npi +- cos^(-1)1/3, n=0, +-1, +-2`,..............
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