Question

prove that sin theta minus cos theta + 1 whole divided by sin theta + cos theta minus 1 is equal to 1 by sec theta minus tan theta using the identity sec squared theta is equal to 1 + tan squared theta​

Answer 1

Step-by-step explanation:

let the theta be (a)

L.H.S =>sin(a)-cos(a)+1/sin(a)+cos(a)+1

num.&denom.is divided by cos(a) ,we get

=> tan(a)+sec(a)-1/tan(a)+sec(a)+1

putting the value of '1' in denom.

=> tan(a)+sec(a)-1/tan(a)+sec(a)+{sec^2(a)-tan^2(a)}

=> tan(a)+sec(a)-1/{sec(a)-tan(a)} {tan(a)+sec(a)-1}

=>1/sec-tan