Question

tanA+secA-1/tanA-secA+1= 1-sinA/cosA=4

Answer 1

Hello!

$\bf{(L.H.S.)}$

$\dfrac{\sf tanA + secA -1}{\sf tanA - secA + 1} \\ \\ \implies \dfrac{\sf tanA + secA + tan^{2}A - sec^{2}A}{\sf tanA - secA + 1} \\ \\ \implies \dfrac{\sf tanA + secA + (tanA + secA)(tanA - secA)}{\sf tanA - secA + 1} \\ \\ \implies \dfrac{\sf (tanA + secA)( 1 + tanA - secA)}{\sf tanA - secA + 1} \\ \\ \implies \sf tanA + secA \\ \\ \implies \dfrac{\sf sinA}{\sf cosA} + \dfrac{1}{\sf cosA} \implies \red{\bf{\dfrac{\sf 1+sinA}{\sf cosA}}}$

$\bf{(R.H.S.)}$

Cheers!