Is cos(x)cot(x)=(1-sin^2(x))/(sin(x)) ?

The answer to whether cos(x)cot(x)=(1-sin^2(x))/(sin(x)) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos(x)cot(x)=(1-sin^2(x))/(sin(x))

prove

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

True

Solution steps

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

Manipulating left side

cos (x) cot (x)

Express with sin, cos

cos (x) cot (x)

Use the basic trigonometric identity:

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

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

Simplify

cos (x) \frac{cos ( x )}{sin ( x )} : \frac{cos ^{2} ( x )}{sin ( x )}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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

cos (x) cos (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= cos^{2} (x)

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

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

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

Rewrite using trig identities

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

Use the Pythagorean identity:

cos^{2} (x) + sin^{2} (x) = 1

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

2 sin^{2} (x) + cos (2 x) = 1

2 cot (4 x) = cot (2 x) - tan (2 x)

sin (2 x) - cot (x) = - cot (x) cos (2 x)

\frac{1 + sec ( x )}{sin ( x ) + tan ( x )} = csc (x)

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

Is cos(x)cot(x)=(1-sin^2(x))/(sin(x)) ?
The answer to whether cos(x)cot(x)=(1-sin^2(x))/(sin(x)) is True