Best solutions to - "How to simplify sin⁡(x)tan⁡(x)+cos⁡(x)?"

bakouninetov

Answered question

2023-01-05

How to simplify

\sin (x) \tan (x) + \cos (x)

Steinunniqhd

Beginner2023-01-06Added 9 answers

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

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

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

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

= \frac{1}{\cos (x)}

= \sec (x)

Kason Wong

Beginner2023-01-07Added 3 answers

We have:

\sin x \tan x + \cos x

= \cos x (\frac{\sin x}{\cos x} \cdot \tan x + 1)

= \cos x (\tan x \cdot \tan x + 1)

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

= \cos x \cdot \sec^{2} x

(p u \in g (\tan^{2} x + 1) = \sec^{2} x)

= \sec x (p u \in g \cos x \cdot \sec x = 1)

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