Find out the answer to "Solve sin⁡(2x)−tan⁡(x)"

Joseph Krupa

Answered question

2021-12-11

Solve

\sin (2 x) - \tan (x)

Suhadolahbb

Beginner2021-12-12Added 32 answers

f (x) = \sin (2 x) - \tan (x) = 2 \sin (x) \cos (x) - \frac{\sin (x)}{\cos (x)}

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

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

As we know

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

f (x) = \frac{\sin (x) \cos (2 x)}{\cos (x)} = \tan (x) \cos 2 x

sonorous9n

Beginner2021-12-13Added 34 answers

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

= \frac{2 \tan (x) - \tan (x) - \tan^{3} (x)}{1 + \tan^{2} (x)}

= \frac{\tan (x) - \tan^{3} (x)}{1 + \tan^{2} (x)}

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

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

= \tan (x) \times \cos (2 x)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?