Check the solution to "How do you simplify tan24b−sec24b"

Yahir Haas

Answered question

2022-01-21

How do you simplify

\tan^{2} 4 b - \sec^{2} 4 b

bemolizisqt

Beginner2022-01-22Added 16 answers

Call

x = 4 b

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

= (\frac{s e \in x}{\cos x} - \frac{1}{\cos x}) (\frac{\sin x}{\cos x} + \frac{1}{\cos x})

= \frac{(\sin x - 1) (\sin x + 1)}{\cos^{2} x} = - \frac{1 - \sin^{2} x}{\cos^{2} x}

= - \frac{\cos^{2} x}{\cos^{2} x} = - 1

Jason Olsen

Beginner2022-01-23Added 14 answers

An alternate solution using the Pythagorean Identity:
We know that

\tan^{2} (x) + 1 = \sec^{2} (x)

Let's let

4 b = x

\tan^{2} (4 b) + 1 = \sec^{2} (4 b)

\tan^{2} (4 b) - \sec^{2} (4 b) = - 1

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