Solve the trigonometry equation in rational form. tan2xsin2x1−sin2xcos⁡2x+cot2xcos2x1−cos2xcos⁡2x+2sin2xtan2x+cot2x=32 What I thought: tan2xsin2x1−sin2xcos⁡2x+cot2xcos2x1−cos2xcos⁡2x+2sin2xtan2x+cot2x−32=0 Transform each fraction into tan⁡x, then you can factor out (tan⁡x−1)2(tan⁡x+1)2

Hint: If cos2x=t then you have: sin2x=1−t tan2x=1−tt cot2x=t1−t and cos⁡2x=2t−1

Answered: "Solve the trigonometry equation in rational form. tan2xsin2x1−sin2xcos⁡2x+cot2xcos2x1−cos2xcos⁡2x+2sin2xtan2x+cot2x=32..."

Jamarion Kerr

2022-01-23

Solve the trigonometry equation in rational form.

\frac{\tan^{2} x \sin^{2} x}{1 - \sin^{2} x \cos 2 x} + \frac{\cot^{2} x \cos^{2} x}{1 - \cos^{2} x \cos 2 x} + \frac{2 \sin^{2} x}{\tan^{2} x + \cot^{2} x} = \frac{32}{}

What I thought:

\frac{\tan^{2} x \sin^{2} x}{1 - \sin^{2} x \cos 2 x} + \frac{\cot^{2} x \cos^{2} x}{1 - \cos^{2} x \cos 2 x} + \frac{2 \sin^{2} x}{\tan^{2} x + \cot^{2} x} - \frac{32}{=} 0

Transform each fraction into

\tan x

, then you can factor out

{(\tan x - 1)}^{2} {(\tan x + 1)}^{2}

fumanchuecf

Beginner2022-01-24Added 21 answers

Hint:
If

\cos^{2} x = t

then you have:

\sin^{2} x = 1 - t

\tan^{2} x = \frac{1 - t}{t}

\cot^{2} x = \frac{t}{1 - t} and

\cos 2 x = 2 t - 1

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?