How do you prove 1/(sinxcosx) - cosx/sinx = tanx?

2 Answers
Jun 26, 2018

Kindly see a Proof in Explanation.

Explanation:

1/(sinxcosx)-cosx/sinx,

=1/(sinxcosx)-cosx/sinx*cosx/cosx,

=(1-cos^2x)/(sinxcosx),

=sin^2x/(sinxcosx),

=sinx/cosx,

=tanx, as desired!

BONUS :

1/(sinxcosx)-cosx/sinx=2/(2sinxcosx)-cotx=2/(sin2x)-cotx.

:. 1/(sinxcosx)-cosx/sinx=tanx rArr 2csc2x-cotx=tanx.

Jun 26, 2018

As proved below.

Explanation:

"To prove " 1 / (sin x cos x) - cos x / sin x = tan x

L H S = 1 / (sin x cos x) - cos x / sin x

=> (1 - cos x * cos x) /( sin x cos x), " taking " sin x cos x " as L C M"

=>. (1 - cos^2 x) / (sin x cos x), color(crimson)(" identity " sin^2x + cos^2x = 1

=> sin^2 x / (sin x cos x)

=> sin x / cos x = tan x = R H S