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if 3sec^4theta + 8 = 10sec^2theta , then...

if `3sec^4theta + 8 = 10sec^2theta` , then find the value of `tantheta`

Text Solution

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`sec^2theta-tan^2theta=1`
`sec^2theta=1+tan^2theta`
`3(sec^2theta)^2+8=10sec^2theta`
`3(1+tan^2theta)^2+8=10(1+tan^2theta)`
`Let tan^2theta=t`
`3(1+t)^2+8=10(1+t)`
`3(1+t^2+2t)+8=10+10t`
`3+3t^2+6t+8=10+10t`
...
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