Question #58cc8

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Answer 1 · 2016-07-27T16:57:41

see explanation

Rewrite as:

#cos^2(x)(1 +cos^2(x)) = 1#

Divide both sides by #cos^2(x)#:

#1+cos^2(x) = sec^2(x)#

Take #sin^2x + cos^2x =1# and divide by #cos^2x# to get:

#tan^2x + 1 = sec^2x#

#implies 1 + cos^2(x) = 1 + tan^2(x)#

#implies cos^2(x) = tan^2(x)#

Divide by #cos^2(x)# both sides:
#1 = tan^2(x)*1/cos^2(x)#
or
#1 = tan^2(x)*sec^2(x)#

#therefore# statement becomes

#tan^2(x)(1+tan^2(x)) = 1#

#implies tan^2(x) + tan^4(x) = 1# as required