Prove the trigonometric identity? #tanx(1-cot^2x)+cotx(1-tan^2x)=0#

2 Answers
Jul 17, 2016

Prove trig identity.

Explanation:

Replace in the equation #tan x = (sin x)/(cos x)#, and #cot x = (cos x)/(sin x)#
#(sin x)/(cos x)(1 - (cos^2 x)/(sin^2 x)) + (cos x)/(sin x) (1 - sin^2 x/(cos^2 x)) =#
#(sin x)/(cos x) - (cos x)/(sin x) + (cos x)/(sin x) - (sin x)/(cos x) = 0# OK

Jul 17, 2016

Applying identity #tanxcotx=1#

#LHS=tanx(1-cot^2x)+cotx(1-tan^2x)#

#=tanx-tanxcot^2x+cotx-cotxtan^2x#

#=tanx-1*cotx+cotx-1*tanx#

#=0=RHS#

Proved