 Hello and how are you all today? The question says prove that secant a bracket 1 minus sin a bracket closed, bracket open secant a plus tan a bracket closed is equal to 1. So let us start with the left hand side of the question. So we have secant a 1 minus sin a secant a plus tan a is equal to 1. Right now we can write secant a as sorry here we were writing only the left hand side. We can write secant a as 1 upon cos a here also and here we can write secant a as 1 upon cos a and tan a as sin a upon cos which can be written now as 1 minus sin a upon cos a into 1 plus sin a upon cos a. Now on multiplying we get 1 minus sin a into 1 plus sin a upon cos square a. a minus b a plus b is a square minus b square where a is 1 and b is sin a. So it will be 1 minus sin square a upon cos a which is further equal to we know that 1 minus sin square theta is equal to cos square theta right. So we can write here cos square a upon cos square a which on simplifying gives us the answer as 1 which is the right hand side right. So hence we have proved the given trigonometric question. So hope you understood it. Enjoyed it. Have a nice day.