Question

Evaluate lim x tends to π/2 (secx - tanx)

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Answer 1

Step-by-step explanation:

LIMIT. (secx - tanx)

x->π/2

lim. (1/cosx - sinx/cosx)

x->π/2

lim. ((1-sinx)/cosx)

x->π/2

lim

Answer 2

$lim_{x - > \frac{\pi}{2} }(secx - tanx)(\frac{secx+tanx}{secx+tanx} )\\\\ =lim_{x - > \frac{\pi}{2} }( \frac{sec²x-tan²x}{secx+tanx})\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \\= lim_{x - > \frac{\pi}{2} }( \frac{1}{\frac{1}{cosx}+\frac{sinx}{cosx}} ) \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\\\ =lim_{x - > \frac{\pi}{2} }( \frac{cosx}{1+sinx} )\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\\\ =\frac{ \cos( \frac{\pi}{2} ) }{ 1+\sin( \frac{\pi}{2} ) } = \frac{0}{1+1} =0\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$