Question

Which of these equation does not have a solution?

• A. $5\sin \left(x\right)=4.9$
• B. $4\cot \left(x\right)=400$
• C. $3\tan x=0$
• D. $\sec x=-1/2$
• E. $\cos x=-0.001$

Answer 1

The correct option is D $\sec x=-1/2$

Given

$5\sin x=4.9$

Range of $\sin x$ is $[-1,1]$

$⟹$ Range of $5\sin x=[-5,5]$

$4.9\in [-5,5]$

$4\cot x=400$

Range of $\cot x$ is $400$

$⟹$ Range of $4\cot x=R$

$400\in R$

$3\tan x=0$

Range of $\tan x$ is $R$

$⟹$ Range of $3\tan x=R$

$0\in R$

$\sec x=-1/2$

$⟹\cos x=-2$

Range of $\cos x$ is $[-1,1]$

$-2\notin [-1,1]$

$\cos x=-0.001$

Range of $\cos x$ is $[-1,1]$

$-0.001\in [-1,1]$

So $⟹\sec x=-1/2$ doesnot have a Solution.