Lim x tends to π/2(x tanx-π/2secx)
Answers
Answered by
2
Lim x --> (pi/2)( sec(x) - tan(x))
lim x-->pi/2 ((1-sin x)/cos x) = lim x-->pi/2 ((1-sin x)(cos x))/ cos^2 x
=lim x-->pi/2 ((1-sin x) cos x)/( 1-sin ^2 x) = lim x-->pi/2 (1-sin x)(cos x)/((1-sin x)(1+sin x))
=lim x-->pi/2 ((cos x)/(1+sin x)) = cos (pi/2)/((1+ sin(pi/2)) = 0/(1+1) = 0
lim x-->pi/2 ((1-sin x)/cos x) = lim x-->pi/2 ((1-sin x)(cos x))/ cos^2 x
=lim x-->pi/2 ((1-sin x) cos x)/( 1-sin ^2 x) = lim x-->pi/2 (1-sin x)(cos x)/((1-sin x)(1+sin x))
=lim x-->pi/2 ((cos x)/(1+sin x)) = cos (pi/2)/((1+ sin(pi/2)) = 0/(1+1) = 0
Similar questions