Expert answers to "What is the formula of 1-cosxsinx?"

chatlibrecc3

Answered question

2022-12-18

What is the formula of

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

anagenezatmy

Beginner2022-12-19Added 4 answers

Find the equation for

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

.
It is known that

1 - c o s (2 θ) = 2 s i n^{2} θ

and

s i n (2 θ) = 2 s i n θ c o s θ

.
So,

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

and

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

.
Replace the values in the expression

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

and simplify:

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

Therefore, the equation for

\frac{1 - \cos x}{\sin x} is \tan (\frac{x}{2})

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