Question

Question #efef9

Answer 1

`sqrt(1-sinx)=sin(x/2)-cos(x/2)`

Explanation:

`sqrt(1-sinx)=sqrt(sin^2(x/2)+cos^2(x/2)-2.sin(x/2)cos(x/2)` `color(green)([As.sin^2theta+cos^2theta=1andsin2theta=2sinthetacostheta])`

`=sqrt((sin(x/2)-cos(x/2))^2` `color(red)([As.a^2+b^2-2ab=(a-b)^2=(b-a)^2])`

`=sin(x/2)-cos(x/2)` `color(brown)((Ans.))`