Hello!
The correct answer is: D. [tex]cscx(\frac{\pi }{2}-x)=\frac{1}{sin\frac{\pi }{2} *cosx-cos\frac{\pi }{2} *sinx}=secx[/tex]
Why?
Let's put a letter to each option in order to make the explanation easier:
First option will be A
Second option will be B
Third option will be C
Fourth option will be D
So,
First we need to know that:
[tex]cscx=\frac{1}{sinx}[/tex]
and
[tex]sin(x-y)=sinx*cosy-cosx*siny[/tex]
Therefore:
[tex]secx=\frac{1}{sin(\frac{\pi }{2}-x) }=\frac{1}{sin\frac{\pi }{2} *cosx-cos\frac{\pi }{2} *sinx}=secx[/tex]
[tex]secx=\frac{1}{1*cosx-0 *sinx}=\frac{1}{cosx}=secx[/tex]
Then,
[tex]secx=secx=cscx(\frac{\pi }{2}-x)[/tex]
Have a nice day!
