1.

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

Answer» `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`
`3t^2+(6t-10t)+(8+3-10)=0`
`3t^2-4t+1=0`
`3t^2-3t-t+1=0`
`3t(t-1)-1(t-1)=0`
`(t-1)(3t-1)=0`
`t=1,1/3`
`tan^2theta=1,1/3`
`tantheta=pm1,pm1/sqrt3`
`tantheta=1,-1,1/sqrt3,-1/sqrt3`.


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