If sin theta -cos theta=1/2 then find the value of 1/sin theta +cos theta

Question

Plase help in my maths b3cause mey maths is weak and tell answe4 as soon as possibli because it is my mother mobile

Answer 1

third identical submission by Aryan.  ALREADY ANSWERED BY BOBOSHARIF.

Answer 2

sin(x)-cos(x)=1/2 (*)

1/(sin(x)+cos(x))=?

 

1/(sin(x)+cos(x))=(sin(x)-cos(x))/(sin²(x)-cos²(x))=(1/2)/(-cos(2x))

From (*) it follows that 1-sin2(x)=1/4 (by taking square from sides)

sin(2x)=1-1/4=3/4

cos(2x)=√(1-9/16)=√7/4.

Therefore

1/(sin(x)+cos(x))=(1/2)/(-√7/4)=-2/√7.