Best solutions to - "How to simplify tan⁡x1−cos2x?"

Destiney Barrett

Answered question

2023-01-16

How to simplify

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

Mikayla Cox

Beginner2023-01-17Added 15 answers

\frac{\tan x}{1 - \cos^{2} x} = \frac{\tan x}{\sin^{2} x} = \frac{\frac{\sin x}{\cos x}}{\sin^{2} x} = \frac{\sin x}{\cos x} \cdot \frac{1}{\sin^{2} x}

= \frac{1}{\sin x \cos x}, or, = \sec x \csc x

Since,

\sin 2 x = 2 \sin x \cos x, t h e a b o v e c a n f u r t h e r b e \exp r e s s e d a s \frac{2}{2 \sin x \cos x} = 2 \csc 2 x

porfiru1nm

Beginner2023-01-18Added 1 answers

\tan x = \frac{\sin x}{\cos x}

You only need to keep in mind one identity:

\sin^{2} x + \cos^{2} x = 1

all the others can be deduced from this
So

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

Hence the original expression can be written as

\frac{\sin x}{\cos x \sin^{2} x}

Cancelling gives

\frac{1}{\sin x \cos x}

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