In Exercises 33 and 34, fill in the missing step(s). 33. sec4 x 2 sec2 x + 1 = (sec2 x

Chapter 6, Problem 34

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Verifying a Trigonometric Identity In Exercises 33 and 34, fill in the missing step(s).

\(\frac{\tan x-\cot x}{\tan x+\cot x}=\frac{\frac{\sin x}{\cos x}-\frac{\cos x}{\sin x}}{\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}}\)

                                                     = __________

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

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

                                                     = __________

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

Text Transcription:

tan x - cot x/tan x + cot x = sin x/cos x - cos x/sin x / sin x/cos x + cos x/sin x

= sin^2 x - cos^2 x / 1

= sin^2 x - cos^2 x

= 1 - 2 cos^2 x

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