Verify each identity a secbeta tanbeta 1secbetatanbeta Sol

Verify each identity: a) secbeta + tanbeta = 1/secbeta-tanbeta

Solution

lets ratinalize and multiply numerator and denominator by sec b+tan b,

we get,

(sec b+tan b)/(sec b+tan b)(sec b-tan b)

(sec b+tan b)/sec^2 b-tan^2b

and we know sec^2 b-tan^2b=1

so RHS=sec b+tan b,

hence proved