Question

How do you verify the identity `secx-cos^2xcscx=tanxsecx`?

Answer 1

This equation is not correct if you pick a value for x say `pi/3`and plug it in to both sides then you can see that it is not a true statement.

Answer 2

The equation is not true.

Explanation:

Check if the equation is true or not by computing the left side, then the right side:

Left Side:
`secx-cos^2xcscx`
`=1/cosx-cos^2x/sinx`
`=frac{sinx-cos^2xcosx}{cosxsinx}`
`=frac{sinx-cos^3x}{cosxsinx}`

Right Side:
`tanxsecx`
`=sinx/cosx*1/cosx`
`=sinx/cos^2x`

The equation above is not true because the left side of the equation is not equal to the right side of the equation:
`frac{sinx-cos^3x}{cosxsinx}cancel(=)sinx/cos^2x`