Question

Sec(x)-tan(x)=1/sec(x)+tan(x)

Answer 1

Answer:

Step-by-step explanation:

I assume that you mean

sec(x)-tan(x) = 1 / ( sec(x) + tan(x) ) , right ?

then this is equivalent to

[ sec(x) - tan(x) ] x [ sec(x) + tan(x) ] = 1

let s evaluate it, we got

sec2(x) - sec(x)tan(x) + - sec(x)tan(x) - tan2(x) = sec2(x) - tan2(x)

= (1 - sin2(x) ) / cos2(x) = cos2(x) / cos2(x) = 1

as cos2(x) + sin2(x) = 1