Can y'all check my answer?

Question

asked Aug 10, 2020 174k views

1 Answer

Mujimu · Answer 1 · 2020-08-16T17:46:26+0000

$\cos x\tan x=\sec x\iff\cos x(\sin x)/(\cos x)=\sec x\iff\sin x=\sec x$

Multiply both sides by
$\cos x$ to get

$\sin x\cos x=1$

Recall the double angle identity for sine to write this as

$\frac12\sin2x=1\implies\sin2x=2$

But
$-1<\sin x<1$ for all
, which means there are no
for which
$\cos x\tan x=\sec x$ holds true. So all the options are indeed counter-examples.