Question

solve algebraically and prove if it is or is not an identity
secx+cscx=1

Answer 1

\[\begin{align*}
\sec x+\csc x&=\frac{1}{\cos x}+\frac{1}{\sin x}\\\\
&=\frac{\sin x}{\sin x\cos x}+\frac{\cos x}{\sin x \cos x}\\\\
&=\frac{\sin x+\cos x}{\sin x\cos x}
\end{align*}\]
For the right hand side to simplify to \(1\), you need to show that
\[\sin x+\cos x=\sin x\cos x\]
Is this true?

Answer 2

No, it is not