Question

Prove that: $\sec x\sqrt{1-{\sin }^{2}x}=1$

Answer 1

We know that ${\cos }^{2}x+{\sin }^{2}x=1$

$\Rightarrow {\cos }^{2}x=1-{\sin }^{2}x$

$\Rightarrow \sec x\sqrt{1-{\sin }^{2}x}=\sec x\left(\cos x\right)=\frac{1}{\cos x}\left(\cos x\right)=1$