Question

1=(1-sin^2O)(1+tan^2O)

Answer 1

I believe the equation is

`1=(1-\sin^2\theta)(1+\tan^2\theta)`

which is true for all
`\theta`, so I guess you're supposed to show why (i.e. establish the identity). Recall that

`\cos^2\theta+\sin^2\theta=1`

from which we can derive

`\cos^2\theta=1-\sin^2\theta`

`1+\tan^2\theta=\sec^2\theta`

So the original equation is equivalent to

`1=\cos^2\theta\sec^2\theta`

and since
`\sec\theta=\frac1{\cos\theta}`, the right side reduces to 1.