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The general value of theta satisfying th...

The general value of `theta` satisfying the equation `tan^2theta+sec2theta=1` is_____

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The correct Answer is:
`thetampi, npi pm (pi)/(3)`
Given , `tan^(2) theta + sec 2 theta = 1`
`rArr tan^(2) theta + (1)/(cos^(2) theta) = 1`
` rArr tan^(2) theta+(1+tan^(2)theta)/(1-tan^(2) theta) = 1`
`rArr tan^(2) theta (1-tan^(2) theta) + (1+tan^(2) theta) = 1-tan^(2) theta`
`rArr 3tan^(2) theta - tan^(4) theta = 0`
`rArr tan^(2) (3-tan^(2)theta) = 0`
`rArr " "tan theta =0`
`rArr" " tan theta = pm sqrt(3)`
Now, `tan theta = 0 rArr theta = mpi`, where m is an integer.
and `tan theta = pm sqrt(3)= tan (pm(pi)/(3))`
`rArr" "theta = npi pm (pi)/(3)`
`therefore theta = mpi, npi (pi)/(3)`, where m and n are integers.
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