Question

Prove the identity sinxtanx + sinx/yanx = 1/cosx

Answer 1

\[\sin(x)\sin(x)/\cos(x)+\sin(x)\cos(x)/\sin(x)=(\sin^2(x)/\cos(x))+(\cos(x))=\sin^2(x)+\cos^2(x)/\cos(x)=1/\cos(x)\]

Answer 2

\[\tan(\theta) = \frac{ \sin(\theta) }{ \cos(\theta) }\]
\[\sin(\theta)\frac{ \sin(\theta) }{ \cos(\theta) } + \sin(\theta)\frac{ \cos(\theta) }{ \sin(\theta) }\]
\[\frac{ \sin(\theta)^2 }{ \cos(\theta) } + \cos(\theta) \rightarrow \frac{ \sin(\theta)^2 }{ \cos(\theta) } + \frac{ \cos(\theta)^2 }{ \cos(\theta) } \rightarrow \frac{ \sin(\theta)^2 + \cos(\theta)^2 }{ \cos(\theta) } \rightarrow \frac{ 1 }{ \cos(\theta) }\]