Question

prove the trig functions
and show the steps

0=theta when i write this

6. sec0/tan0=csc0
7. (sec x +tan x)(1-sin x/cos x)=1
8. 2/sqrt3 cosx+sinx=sec(pi/6-x)
9. prove tan(0/2)=sin0/1+cos0 for 0 in quadrant 1 by filling in the reason belo

Answer 1

\[\frac{\sec \theta}{\tan \theta}=\csc \theta\]
\[\frac{1}{\cos \theta}\over\frac{\sin \theta}{\cos \theta}\]
\[(\frac{1}{\cos \theta})\times \cos \theta \over(\frac{\sin \theta}{\cos \theta} )\times \cos \theta\]

Answer 2

\[\frac{1}{\sin \theta}=\csc \theta\]

Answer 3

\[(secx+tanx)(\frac{1-sinx}{cosx})=1\]
\[(\frac{1}{cosx}+\frac{sinx}{cosx})(\frac{1-sinx}{cosx})\]
\[\frac{1-sinx}{\cos ^{2}x}+\frac{sinx-\sin ^{2}x}{\cos ^{2}x}\]
\[\frac{1-sinx+sinx-\sin ^{2}x}{\cos ^{2}x}\]
\[\frac{1-\sin ^{2}x}{\cos ^{2}x}\]
\[\frac{\cos^2x}{\cos^2x}=1\]

Answer 4

Can't tell what you mean by the third one. Don't know if sinx is part of the denominator or not.