Question

Prove this trigonometric equation;

- tan^2x + sec^2x = 1,

Answer 1

Hey there :)

- tan²x + sec²x = 1 or 1 + tan²x = sec²x

sin²x + cos²x = 1
Divide the whole by cos²x


`(sin^2x)/(cos^2x) + (cos^2x)/(cos^2x) = (1)/(cos^2x)`


`(sinx)/(cosx) = tanx` so
`(sin^2x)/(cos^2x) = tan^2x`
and

`(1)/(cosx) = secx` so
`(1)/(cos^2x) = sec^2x`

Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}

1 = - tan²x = sec²x or sec²x - tanx = 1