Question

prove that 1/(secA-sinA)=(1+sinA)/cosA​

Answer 1

Answer:

$\red { \frac{(1 + sinA)}{cosA}}\green { = \frac{1}{(secA - tanA)}}$

Step-by-step explanation:

$RHS = \frac{(1 + sinA)}{cosA}$

$= \frac{1}{cosA} + \frac{sinA}{cosA}$

$= secA + tanA$

$= \frac{(secA+tanA)(secA-tanA)}{(secA - tanA)}$

$= \frac{sec^{2}A - tan^{2}A}{(secA - tanA)}$

$= \frac{1}{(secA - tanA)}$

$= LHS$

Therefore.,

$\red { \frac{(1 + sinA)}{cosA}}\green { = \frac{1}{(secA - tanA)}}$