How do you verify csc^2xcot^2x+csc^2x=csc^4x ?

2 Answers

Take #csc^2(x)# common then it becomes:

#csc^2(x)#(1+ #cot^2(x)#)

which is equal to #csc^4(x)#

Explanation:

Basic trigonometric identities
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To prove #(csc^2x cot^2x + csc^2 x) = csc^4 x#

Taking common term #csc^2 x# on L H S out,

#=> csc^2 x ( 1 + cot^2 x) #

But #csc^2 x = 1 + cot^2 x# (Trigonometric identity.)

Hence #=> csc^2 x * csc^2 x = csc^4 x = R H S#

Q E D.

Mar 5, 2018

It is given that, #csc^2xcot^2x+csc^2x=csc^4x #

#LHS=>1/sin^2x* cos^2x/sin^2x + 1/sin^2x#

#cos^2x/sin^4x + sin^2x/sin^4x#

#(cos^2x + sin^2x)/sin^4x#

#1/sin^4x = csc^4x#; [as we know #color(red)(sin^2x + cos^2x = 1#]