How do you verify $csc^2 θ + sec^2 θ = csc^2 θsec^2 θ$ ?

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Answer 1 · 2018-08-10T03:53:50

$csc^2 θ + sec^2 θ = csc^2 θsec^2 θ$

Since $1+tan^2theta=sec^2theta$ :
$csc^2 θ + sec^2 θ = csc^2 θ(1+tan^2theta)$

$csc^2 θ + sec^2 θ = csc^2 θ+csc^2thetatan^2theta$

Since $csctheta=1/sintheta$ and $tantheta=sintheta/costheta$ :

$csc^2 θ + sec^2 θ = csc^2 θ+1/sin^2theta*sin^2theta/cos^2theta$

$csc^2 θ + sec^2 θ = csc^2 θ+1/cancel(sin^2theta)*cancel(sin^2theta)/cos^2theta$

$csc^2 θ + sec^2 θ = csc^2 θ+1/cos^2theta$

Since $sectheta=1/costheta$ :

$csc^2 θ + sec^2 θ = csc^2 θ+sec^2theta sqrt$

How do you verify csc^2 θ + sec^2 θ = csc^2 θsec^2 θcsc^2 θ + sec^2 θ = csc^2 θsec^2 θ?