How do you simplify #tan^2 4b - sec^2 4b#?

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Answer 1 · 2015-06-02T02:36:40

Call x = 4b

#f(x) = (tan x - sec x)(tan x + sec x)#

#= (sin x/cos x - 1/cos x)(sin x/cos x + 1/cos x)#

#= ((sin x - 1)(sin x + 1))/(cos^2 x)# =# - (1 - sin^2 x)/cos^2 x#=

#= - (cos^2 x)/(cos^2 x) = -1#

Answer 2 · 2015-06-02T04:00:37

An alternate solution using the Pythagorean Identity:

We know that #tan^2(x)+1=sec^2(x)#

Let's let #4b=x#

#tan^2(4b)+1=sec^2(4b)#

#tan^2(4b)-sec^2(4b) = -1#