secx * cosecx - cotx =
tanx
We know that:
secx =
1/cosx
csecx = 1/sinx
cot =
cosx/sinx
tanx = sinx/cosx
Now
substitute:
sec x cosec x - cot x = tan x
(1/sinx)*(1/cosx) - (cosx/sinx) =
sinx/cosx
1/sinx*cosx - cosx/sinx =
sinx/cosx
(1- cos^2x)/sinx*cosx =
sin/cos
But we know that: sin^2 x + cos^2x =
1
==> 1-cos^2x = sin^2
x
==> sin^2 x /sin*cos =
sin/cos
==> sinx /cosx =
sinx/cos
==> tanx = tan x
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